The Belgian international has been watched on several occasions by Villa and now Lambert is poised to step up his interest before the transfer window shuts on Friday.
Benteke has netted three times in five games this season after being on target 18 times during the 2011-12 campaign in all competitions.
He also scored for his country for the first time in the 4-2 win over Holland earlier this month on what was his fifth appearance.
Lambert has already signed the Feyenoord duo of central defender Ron Vlaar and midfielder Karim El Ahmadi this summer.
Now he is hoping to purchase Benteke who has three years remaining on his contract although sources close to Villa insist it is "far from being a done deal".
Former Standard Liege player Benteke has the physical presence that Villa have lacked up front since Emile Heskey parted company with the club at the end of last season.
Number one striker Darren Bent has often looked isolated in the opening two Barclays Premier League matches with West Ham and Everton which both ended in defeat.
Source: PA
Source: PA