If you were to make an adhesive, you would have to determine how it would function. You wouldn't want the adhesive to corrode in the body since you would want to keep the medical device in place. There are already medical papers that exist that contain information about medical adhesives and sutures but it seems that they are temporary or are used just to bond to the medical devices outside of the body. Panacol- USA is a company that creates medical adhesives that are used in different types of medical devices and would be a good place to start. Also, there is an article on pubmed called "Clinical Applications of Surgical Adhesives and Sealants" by Lindsey Sanders and Jiro Nagatomi that also could provide some insight.

Ii believe that most of these adhesives would start at Class III especially since it would need to bind to the medical device as well as the patient's bone or tissue using this adhesive. I would it would need to be determined whether you want the adhesive to dissolve gradually over time, if you want it to quickly dissolve or if you want something more permanent. If it dissolves over time, it has to be determined that what it is dissolving is safe in the human body and will be dispelled easily. If you want it more permanent, then it would have to be determined that it is biocompatible and how long would it take until it needs to be replaced or if it needs to be replaced. 

I agree with knm7, but it is important to mention that the FDA determines its' classifications based on factors such as indications for use (see example: https://www.accessdata.fda.gov/cdrh_docs/pdf13/K132243.pdf) which means that the product should have a label that outlines the same details. Given the adhesive is going into the body there could be risk to the patient such as rejection, therefore, it is more likely to receive a higher classification but without knowing the actual application it is difficult to say.

For internal surgical use, I don't see much leeway to be classified anything other than a Class III medical device. Unless it is designed to be metabolized or there is any other chemical mechanism of action besides adhesion, I see it being classified as a medical device (consistent with @mmodi's indications for use argument and @knm7's historical precedent for such devices). The FDA recently listed a guidance document for adhesives (link below). They specify resorbable here, which would increase the risk, but I don't know of any truly inert adhesives for use in the body. Therefore, I don't see much to prevent this from being a Class III device under FDA classification.

Link to the doc: Guidance for Resorbable Adhesion Barrier Devices for Use in Abdominal and/or Pelvic Surgery - Guidance for Industry | FDA

Regulatory affairs protects public health by controlling the safety and efficacy of medical devices. The companies responsible for the discovery, testing, manufacture and marketing of these products that ensure safety. Medical grade adhesives, sealants, coatings and etc. need to be non-toxic and show compatibility with blood and body fluids. Also, they must be biologically safe under two standard tests used to determine their suitability...the U.S. Pharmacopeia (USP) Class VI and/or ISO 10993. Master Bond offers biocompatible compounds that meet one or both specifications. They assure that these product make a worthwhile contribution to public health and welfare most safely.

The classification of an adhesive designed for interna use in medical devices on several factors, including the intended application, the materials used, and how the adhesive will interact with the body. The FDA classifies medical devices in three categories: Class I devices, which are low risk and subject to general controls, Class II, which are moderate-risk and require a premarket notification(510k) and typical have special controls, and Class III devices are high-risk, requiring premarket approval (PMA) due to the significant patient risk.

The intended use of the adhesive is critical to determine what class it falls in to. For instance, surgical adhesives that bond tissues or devices during surgery are considered Class II, as they pose moderate risk to the patients. Alternately, adhesives that chemically interact with body tissue or fluid might be require a Class III classification, especially if the promote tissue healing and have long term implications. Therefore, the difference of how the adhesive interacts in order to achieve its purpose directly influences its regulatory classification.

Today in the US, the FDA classifies medical devices based on their overall risk. Devices that are classified as Class II generally have moderate-risk, including devices like syringes or blood pressure cuffs. These are items in which general control is not sufficient to ensure safety and effectiveness. As for Class III, this class covers high-risk devices that are very important to health and sustaining life. Examples could include pacemakers or deep-brain stimulators. Therefore, the classification of a medical adhesive for internal use would depend both on the characteristics of the adhesive and its intended application. In my opinion, if the adhesive is intended for internal use, such as adhering a medical device inside the body during surgery, it will be classified as a Class III device. The main reason for this classification is that it involves significant risks that are critical to the subjects health such as bio-incompatibility. Furthermore, if the adhesive is being used in critical applications like cardiac or neurological surgeries, even more risk is involved.

On the other hand, an adhesive could also be classified as a drug or a combination product. This is the case if it achieves its primary purpose through chemical interaction with the body, such as through pharmacological or metabolic means. An example of this would be a fibrin sealant. These products, are often used in internal surgeries to help with tissue adhesion by containing proteins that are found in human blood that causes blood to clot. As a result, fibrin sealants require both drug and biologic approval because they involve biological material and work through biochemical processes. Therefore, if the products relies on biological processes, it may be considered a drug or combination product, but the adhesive’s primary mode of action is mechanical, it would likely remain classified as a medical device.