After resigning as Italy boss immediately after his team crashed out of the World Cup at the group stage, the 56-year-old could take over in Istanbul as early as Monday
The 56-year-old left his post as Azzurri boss immediately after they were eliminated from the World Cup group stages, when defeats to Uruguay and Costa Rica ensured they failed to reach the last 16 of the competition.
Meanwhile, the Turkish giants have been looking to recruit a new coach following the departure of Roberto Mancini after they finished second in the Turkish league.
Ousted Manchester United trainer David Moyes had held talks in Istanbul while USA's Jurgen Klinsmann and Germany boss Joachim Low had been name-checked by Galatasaray as top targets.
However, it emerged on Thursday that Prandelli was the new frontrunner after the club announced it was holding talks with the Italian and the club's president has since suggested he will be handed the reins on Monday.
"Cesare Prandelli is a coach who fits our criteria," Aysal is quoted by the club's official Twitter account as saying. "Prandelli and the club will communicate the decision in a day or two, but the Italian is someone that could win the championship with ease.
"On Monday he will be put at the helm of the team and the 2014-2015 season will be beautiful, I can feel it."
Galatasaray will play in the Champions League next year after Fenerbahce were expelled from all European competitions.