The report claims that Galatasaray have held three meetings with Villas Boas and are hoping to appoint him ahead of next season.
In his most recent job, Boas won the Russian league title with Zenit St Petersburg this season but was criticised for playing unattractive football.
The former Chelsea boss guided Zenit to second last season and won the 2014-15 league campaign but the team was knocked out of the Champions League stages.
Villas-Boas has previously coached at Chelsea, Tottenham and enjoyed a successful spell at Porto where he won the Europa League.
Galatasaray are currently enduring one of the worst season’s in their history and are planning major revisions to their squad in the summer.
The Lion’s are currently in sixth place with 44 points in 30 games in the Turkish Super Lig.