Leeds have held talks with Lonergan about a possible switch to Elland Road as they search for a replacement for Kasper Schmeichel.
However, Everton have now entered the race for the 27-year-old custodian.
The Goodison Park club have held a long-term interest in Lonergan with the keeper even training with the Merseysiders last season.
Toffees boss David Moyes is a huge fan of Lonergan having worked with him during his time in charge of Preston and he is hoping to convince him to make the move to the Premier League.
Moyes is in the market for goalkeeping reinforcements after seeing Iain Turner leave the club this summer and Jan Mucha is thought to be considering a move away after growing frustrated with his lack of first-team opportunities.
Lonergan is now weighing up his options as he decides where he sees best to continue his career.
Source: Team Talk
Source: Team Talk