Now an xray can confirm a mass but it cannot tell us what it is (a nasty cancer or benign growth), what it is attached to, or whether we can remove it surgically for a patient. Therefore, if you were keen to have this removed, you may want to have your vet refer you or at least his xrays to a specialist surgeon to see if they could help.
Otherwise, the mainstay of care for anorexia in a cat with a possible abdominal mass would be to see if we can get them eating or facilitate them doing so medically. In regards ***** ***** him to eat, since he is not vomiting, you can try syringe feeding. If doing so, it is ideal to use a critical care diets like Hill's A/D (LINK), Royal Canin Recovery (LINK), or Clinicare Canine/Feline Liquid Diet (LINK) to get nutrition into him. All of these are critical care diets that are calorically dense, so a little goes a long way nutrition-wise. And these could just help get some more calories into him even if we can’t get a huge volume of food in at any one time. And I would note that the liquid diet may be of particular use if he can drink and for fitting past any masses in his GI.
If a cat can physically eat but refuses, we can sometimes fine success with using appetite stimulants like Mertazipine (More Info), so you could speak to his vet about a trial on this.
Finally, if we have a cat that cannot physically eat, then depending exactly where the mass lies, we could consider a feeding tube to bypass this problem area. There are a few options even if we have a stomach mass. The main ones are the Esophagostomy (example, the PEG/Stomach tube (example), or a jejunostomy tube (which communicates with the small intestine). All could be use to bypass a possible stomach mass and would therefore be options for him at this time. Which one would be best your cat will depend on the exact location of the mass and how it is attacked (so how far into the GI is the problem) and the time frame he is suspected to need assisted feeding (since permanent PEG tubes can be placed for cats who may never be able to eat properly again). Once placed, feeding tubes tend to be well tolerated and can be a great means to get around his issue and keep nutrition getting into him.
Overall, this mass is not a positive finding for your lad. Still if he can eat a bit, then the calorically nutritious diets +/- appetite stimulants could help fight his wasting away. Otherwise, it will depend how much you wish to do for your lad. If you are keen to see if this mass can be resected, then do speak to your vets about referral to a specialist surgery. Otherwise, depending just where and how attached the mass is to his GI, you may be able to have a feeding tube in to bypass this growth and support him for as long as possible.
Please take care,