Christian Benteke, Brad Guzan, Fabian Delph and Ashley Westwood have all been linked with moves away from Villa Park, following a disappointing 15th place finish in the Premier League.
Despite constant speculation regarding the future of his star performers, Lambert insists they are not for sale at any price.
"I can say they're not going anywhere. I'll still have the final say on who came and who went," he told the Daily Star.
"I wouldn't imagine anyone will leave without my permission."
The Villa fans have aimed their criticism of the club at Lambert and owner Randy Lerner, who recently announced that the Premier League side is up for sale.
Despite unrest among the supporters, the Scottish manager believes Lerner has done a good job during his eight years at Villa Park.
"You've got to understand and respect the good work he's done here. I don't think that should ever be overlooked," he said.
"But you have to respect, at the same time, he has own things to do."
Following a disappointing season at the foot of the table, Lambert insists he is still enjoying his spell in charge of Villa.
"Any regrets? No, not at all. If it all ended tomorrow I would take away an unbelievable experience because it's a brilliant club," he said.
"The pressure on it is big, no two ways about it. But there's always something good that will come out of something like this.
"So I don't have any regrets."