Sunderland have agreed a fee with Swansea for Danny Graham, Sky sources understand.
City have accepted an offer in the region of ?5m for the striker, who will now undergo a medical and hold talks on Wearside.
Graham has been linked with Sunderland all month after finding his path to the Swansea first team blocked by Michu this season.
Championship side Middlesbrough - the 27-year-old's first club - made a late attempt to hijack the deal on deadline day.
But Graham told Boro he had no interest in dropping out of the Premier League.
The 18-year-old has followed his senior debut in Rovers' final game of last season against Scunthorpe with six further substitute appearances and follows fellow academy graduate Cole Stockton in committing his future to Rovers.
Rovers boss Ronnie Moore said: "I'm delighted to keep Jake at the club for another two seasons.
"He has been really unfortunate not to be involved more this season because of the form of other players, but I really believe he has a big future at Tranmere.
"He's bright and enthusiastic, wants to learn and if he keeps up his hard work in training hopefully it will pay off."
Kirby added: "I'm really pleased to have signed the new contract.
"I've loved being involved with the first-team squad this season and I want to push on over the next couple of seasons and earn a regular place in the team."
