Besiktas have not given up hope of signing Ron Vlaar despite the Netherlands international turning down the Black Eagles last week.
Eurosport TR have claimed that Besiktas will submit a improved offer for the 30-year-old centre back in an attempt to lure him to the Turkish Super Lig.
Vlaar starred at the 2014 World Cup under the stewardship of United boss Louis van Gaal. The Netherlands international has also been closely linked with Southampton.
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.
The 30-year-old provided two assists in 23 appearances for Aston Villa in all competitions this season.
Beşiktaş finished the Turkish Super Lig season in third place and will play in the Europa League next season.