Villa are fast running out of time to convince the 30-year-old to stay, with the centre-back – frequently linked with a reunion with Louis van Gaal at Manchester United – out of contract on June 30.
The Villa Park outfit confirmed on Monday that Vlaar had been offered fresh terms following the club's survival, while Darren Bent was released on a free, joining Derby County permanently.
But it looks increasingly unlikely that Vlaar will remain at Villa, with the Netherlands international claiming he can take a step forward in his career and needs time to assess his options.
"I want to maximise my career and I think I can go a step higher," the Dutchman is quoted as saying in The Mirror. "I will look at it and go quietly."
Vlaar joined the club from Feyenoord in 2012 but has faced a number of injury problems, making 84 appearances in all competitions during his three years in England so far.
Villa are currently facing a degree of uncertainty, with Vlaar stalling on a new deal, Christian Benteke on many Premier League clubs' transfer wishlists and Randy Lerner rumoured to be close to selling the club.