Vlaar joined Villa from Feyenoord on a three-year contract this summer, while fellow Netherlands international Van Persie's future is wrapped up in uncertainty.
Vlaar, though, is hopeful that his compatriot will remain at the Emirates despite being linked with Manchester City and Juventus.
"I really don't know where he is going. I haven't talked to him lately," he told The Mirror.
"I just hope he stays in England so I can face him. I've trained against him with the national team and he is a great player. It would be a big loss if he leaves England."
The 27-year-old also revealed that he had talked to a number players during Euro 2012 in an effort to decide on moving to the Premier League from the Eredivisie.
"I talked to Robin and several other players during the Euros," said Vlaar. "Robin told me if I had the chance then to come over, but it was still my decision and I'm very happy Aston Villa came in for me.
"I'm happy the deal was done. I also talked to Karim (El Ahmadi, also signed by Lambert from Feyenoord) and they all said the Premier League would really suit me."
Villa will begin their Premier League campaign with an away game against West Ham United on Saturday, August 18.