Leeds' academy forward, the younger brother of Newcastle United's Shola, made 10 appearances for Scunthorpe between November and January and has been added to Iron boss' Nigel Adkins' list of transfer targets this summer.
Ameobi played twice for Leeds last season, against Portsmouth in the Carling Cup and again during a Johnstone's Paint Trophy tie at Darlington and Adkins hopes the offer of more regular first-team football will lead him to reject new terms at Elland Road.
Scunthorpe would be forced to pay compensation for a player who is under the age of 24, a factor which may complicate any deal, but Adkins will be ready to act if the teenager decides to move on.
Adkins said: "He's got a bright future in the game. He's 19 years of age, he's 6ft 2in and he's a raw talent. I've tried to bring him to the club. Leeds have offered him a contract, but I can't see him figuring in their team.
"First and foremost we'd have to do a deal with Leeds, and likewise we'd have to make sure there's a position for the player to fill. We'll have to see what happens."