Queens Park Rangers have been linked with a bid for Dutch defender Vlaar, while Newcastle United and Tottenham Hotspur are monitoring Delph, the Daily Star reports.
With the duo entering the final year of their existing contracts and cash-strapped Villa up for sale, there have been reports that Lambert could be forced to offload his key assets.
However, the former Norwich City boss maintains that he still has the final say over who leaves the club and issued a hands-off warning on Delph and Vlaar.
"I don't think anyone will go without me saying so. Put it that way," he told reporters.
"I think the lads are happy here and want to get going again. Things will happen with those lads in the next little bit. It will take course through the season."
Villa's Premier League season gets underway on August 16 when they take on Stoke City away from home.