Baines has 18 months left on his current contract and Everton boss Roberto Martinez is making the England left-back's new deal one of his top priorities.
Baines arrived at Goodison Park from Wigan in 2007 in a deal worth £6m.
His former boss at Everton, David Moyes, twice tried to sign the defender for Manchester United last summer, only to be knocked back.
Martinez also made it clear last month that there was no chance of Baines leaving the club in January after another impressive start to the campaign for Everton.
"In football you don't work long term, you go window to window and I can guarantee that Leighton will be here at the end of the season," Martinez said in December. "That is 100 per cent.
"That is how you work from window to window - to have a stronger squad than previously.
"Leighton is vital for us in the second half of the season. Bryan Oviedo has been terrific, but we need Leighton and Bryan fit for us, if we are going to fight for our football dream."
Everton have signed winger Aiden McGeady from Spartak Moscow already this month as they aim to push on and secure a top-four spot in the Premier League
They are currently back in sixth ahead of Monday night's game away to West Bromwich Albion.