The former England Under-21 forward is currently on loan at Villa Park from Manchester City until the end of the season.
And after scoring two goals in three FA Cup appearances en-route to the Final, the 26-year-old wants to join Tim Sherwood’s side ahead of next season.
Villa celebrate Fabian Delph's goal in the semi-final with Liverpool
"I feel at home at Villa, it's a great club," said the former Chelsea and Swansea City man.
"I'm sure at the end of the season we can sit down and I can sign.
"I just have to wait until the end of the season."
Sinclair will have a forced rest from action this weekend as Villa face his parent club at the Etihad Stadium.
But with Sunday’s Cup semi-final victory over Liverpool still fresh in the memory, Sherwood’s squad will head north with confidence.
Villa skipper Fabian Delph scored the winner at Wembley and he’s a player that has impressed Sinclair since he arrived at the club in January. Delph's decision to sign a new deal at Villa Park is another factor in Sinclair’s future plans.
Both Sinclair and Delph scored in the quarter final against West Brom
"He is performing every week and every week he is improving," he added.
"He's stayed here, signed a new contract and this is his home.
"I think when you are playing every week you go into a place where you get more confident and that's what he's done."
Villa will face Arsenal in the Final at Wembley on Saturday 30 May.
