Uncertainty has surrounded the club recently after owner Randy Lerner confirmed that he is looking to sell Villa, but Lambert believes that his decision will not force him to part company with the likes of Christian Benteke and Fabian Delph.
"I can say they're not going anywhere," the Scot told reporters.
"I'll still have the final say on who came and who went. I'd imagine I'd still have all that on my side.
"I wouldn't imagine anyone will leave without my permission. I think that's fair to say."
Villa confirmed on Wednesday that midfielder Gary Gardner had signed a new deal at the club.