The Netherlands international travelled to England a week ago to hold talks with Villa manager Paul Lambert regarding a possible move to the Premier League.
Vlaar subsequently admitted it would be a 'dream come true' to join Villa, but Feyenoord have not received any contact since the player's meeting with Lambert.
The Dutch club have been critical of Villa over the weekend and coach Ronald Koeman had set a deadline of Monday for their English counterparts to make a decision regarding Vlaar.
Koeman also suggested that he thought the centre-half would be leaving De Kuip, but Vlaar now appears resigned to staying with Feyenoord.
"Feyenoord is in my heart and I have been through a lot here," Vlaar told RTV Rijnmond.
"I think the chance I will move to Aston Villa is not so big anymore.
"I don't want to be kept on a leash, so a transfer is off for now."