Lambert slams disrespectful Koeman
Koeman's admiration for Villa captain Vlaar is no secret and the Dutch manager seems keen on a reunion with the defender, who played for him at Feyenoord.
The St Mary's Stadium manager described Vlaar as a "perfect addition to every group" last week and Lambert has taken aim at him for his comments.
"I think he is disrespecting [Aston Villa] when you are talking about other team's players when they are still their players," Lambert said.
"I think that's wrong.
"I wouldn't mind if he picked up the phone, but you don't go public on it. That's the thing that annoyed me the most and the stance is still exactly the same with Ron."
The 29-year-old defender joined Villa in July 2012 and has been a first-team regular ever since.
And Lambert does not believe the thought a potential move to Southampton is affecting Vlaar.
"I don't have a problem [with Ron]," he added.
"You saw Ron play on Saturday, he was fantastic for us so I don't think anything like that is preying on his mind at all.
"I just thought it was the wrong thing to have done [from Koeman]."
Villa started their Premier League season with a 1-0 win at Stoke City and host Newcastle United on Saturday.