In a meeting of more than three hours, Terim, dubbed "The Emperor", agreed in principle with the club's new management, which was elected Sunday after president Adnan Polat resigned, the mass circulation daily Haber Turk said.
With two more games to be played this season, Galatasaray are currently ninth in the championship, lagging 36 points behind leaders and arch-rivals Fenerbahce.
Winners of the UEFA Cup in 2000 when Terim was previously coach, the Istanbul side have lost all hope of qualifying for European competition next season.
He will make a final decision after consulting with his family, the Hurriyet newspaper reported.
Terim, 57, has been coach at Galatasaray twice during 1996-2000 and 2002-2004.
He has coached Italian teams Fiorentina and AC Milan and then led the Turkish national squad to the semi-finals of the Euro 2008 championship.
In March, Galatasaray sacked coach Gheorghe Hagi, only five months after hiring the Romanian to replace Dutch coach Frank Rijkaard.