The Feyenoord defender, 27, had held talks with Villa boss Paul Lambert over the previous weekend and admitted it would be a "dream" to swap the Eredivisie for the Premier League.
He told De Telegraaf newspaper shortly afterwards: "I was on Sunday in Birmingham to have talks with Paul Lambert and left with a very positive impression.
"Joining Aston Villa would be a dream come true. I look forward to the Premier League but I will miss Feyenoord.
"I feel at home at De Kuip and although both me personally and the club have had a lot of ups and downs, we have maintained a good relationship. The stadium, the fans, my team-mates and staff...if the deal goes through I will miss them."
The move for Vlaar, who has won nine caps for the Netherlands, appears at risk of falling through, however, after negotiations stalled.
Vlaar said to RTV Rijnmond: "Feyenoord is in my heart and I have been through a lot here. 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 transfer is off for now."