The defender has been at Goodison Park for nine years and could see his stay extended further.
Baines has been at Goodison Park for nine years since moving to Merseyside from Wigan Athletic in 2007, and has played nearly 350 competitive first-team games for the Toffees.
However, he struggled with fitness issues last season, with his 18 Premier League appearances representing his lowest tally in a top-flight campaign during his career.
He also had a notable falling out with former manager Roberto Martinez, after quotes attributed to the left-back were published in which Baines was reported to have suggested that there was no team chemistry under the Spaniard.
However, it appears as though new boss Ronald Koeman sees Baines as part of his plans for the club, as the Liverpool Echo claims that the club will open talks imminently over a new deal for the 31-year-old.
If he does indeed sign new terms, it seems likely that the England man will retain his spot as the club's first-choice left-back under the former Southampton manager.
Baines has been a good servant to Everton and is a popular figure amongst most Toffees supporters, both for his attacking style and committed performances, and for turning down several chances to leave the club over the last near-decade.
Reacting on Twitter to the reports, Toffees supporters hailed the defender and the club's apparent decision to keep faith with him.
Leighton Baines new contract— Alan Collins (@CollinsEFC) July 28, 2016
Baines meant to be signing a new deal shortly according to the Echo. Be great news, hopefully the inj problems of last year are behind him— Ghedin1878 (@Ghedin1878) July 29, 2016
Evertonians adore Baines & Coleman. Loyalty shown incredible too. https://t.co/MeQZXXGZc8— FollowEverton.com (@followeverton) July 28, 2016