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Obviously, try taking all the paper out, and seeing if you can get the tray back in while it is empty.
After that - if you can - put only about 20 to 40 sheets of blank paper into it, and see if that works for you, and the drawer gets back in properly as it should.
Let me know more about the problem, how it goes, etc. I will advise further as needed.
What part won't close, please?
A photograph, if you could take one and post one, would explain to me what and where the problem is, perhaps.
A flap or moving part of the drawer may well be protruding.
If your printer were a two-drawer printer, you could try swapping the drawers, and prove whether it's the drawer, or the place it fits into, that is at fault.
Also the space it fits into may be obstructed. Look into it, for anything that might be protruding into that space about 3 inches short of its farthest depth.