The Dutch centre-back, 29, is in the final season of his contract at Villa Park, having moved to the Midlands outfit from Feyenoord in 2012.
Vlaar's representative Arnold Oosterveer said earlier in November that the defender was in demand in mid-year, with Southampton among the suitors, and that it was time for him to "take a nice step".
Lambert hit back at Oosterveer, who also claimed Villa had not approached Vlaar's management, stating the player's agent had gone too far with his comments.
"I'm not blaming Ron in any shape or form. He's been great, [we've had] good dialogue with him but I don't think you can do what he [Oosterveer] did," Lambert told BBC Radio 5 live.
"The options are open for Ron because he's in his last year, but I don't think you should air your views... especially when they're not true.
"All you can do is your best to try and keep him. We are trying our best on that front."
Lambert rubbished Oosterveer's claim the two parties had not met to discuss Vlaar's future beyond the 2014-15 season.
"We have been speaking with Ron and the message from his agent was thanks but no thanks," Lambert said.
"I'd love to keep him. We've put our foot forward and I'm a bit annoyed the agent says the ball is in our court."
Villa host Southampton on Monday, looking to snap a seven-match winless streak - a run in which they have scored just once - while the Saints have won four on the trot.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.