The report claims that Besiktas are preparing a new offer for the 30-year-old after he turned down a move to the Istanbul based club last month.
The former Villa defender whose contract expired at the end of the June has demanded a hefty signing on fee brining up his cost for the first year up to €3 million according to LigTV.
Vlaar starred at the 2014 World Cup under the stewardship of United boss Louis van Gaal. The Netherlands international who joined Villa for €5 million from Feyenoord, is free to talk directly to other clubs with his contract set to run out at the end of the month.
Beşiktaş finished the Turkish Super Lig season in third place and will play in the Europa League next season.