Sources tell us a $909.99 check made payable to Steiner Sports Memorabilia back in 2011 bought D.T. a signed Hank Aaron pic and two photos of Yankees teams from the '50s.

We're told POTUS used to buy memorabilia like that all the time as gifts for clients ... and now, the check he personally signed could be the perfect present for you -- if ya got the cash.

According to RR Auction ... the check is ultra rare -- the first known Trump one to hit the auction block -- and could go for more than what similar modern president checks have sold for recently.

The minimum bid was $500 ... but it's already up over $3,000 -- and still has a nearly a week left on the block.