The former Inter and Manchester City coach is set to sign a three-year contract with the Istanbul giants worth in excess of an annual €5 million
The Italian coach emerged as the leading candidate to replace the legendary Turk over the weekend following his dismissal from the club last week.
Negotiations between the two parties are at an advanced stage, with the only sticking points being Mancini's desire to install his own assistants and have the option to negotiate with an international team.
He will reportedly earn a salary of over €5 million (£4.2m) per year in the Super Lig across the course of a three-year deal, with official confirmation of his arrival expected on Monday.
Terim led Galatasaray to two Turkish titles during the most recent of his three spells in charge of the club, but a falling-out with president Unal Aysal led to his dismissal.
Mancini, meanwhile, has been out of work since being sacked by Manchester City at the end of last season.