Carver, who worked as Sir Bobby Robson's first-team coach at St James' Park and briefly acted as caretaker following his departure in 2004, is currently making his way in the management game at Toronto FC.
And he is hoping to persuade Ameobi, 26, whom he helped to bring through the Academy ranks on Tyneside, that his future lies on the other side of the Atlantic.
Carver said: "I need some firepower up front and I am looking for new players, especially a striker.
"I have got my side organised now and have made Toronto difficult to beat, but I need to sign players in that area.
"Shola is a kid I brought through the system at Newcastle United, and a kid I know an awful lot about.
"If I can get Shola into this football club he would be a huge, huge asset for us."
Ameobi found himself surplus to requirements at Newcastle last season - he started only four games and made just two appearances under new boss Kevin Keegan - and ended the campaign on loan at Stoke.
However, he appears to have rejected the chance to join the newly-promoted Potters on a permanent basis.