Lambert has confirmed Villa are in talks with the 27-year-old player, who spent four seasons with FC Twente before signing for Feyenoord in 2008 for five million euro.
Press Association Sport understands they are close to agreeing a fee for the player in the region of £2.5-£3 million, and Lambert said: "We're in talks at this moment, those talks are ongoing and we hope to reach a positive conclusion with Feyenoord and the player."
He added: "Karim is a player who I feel could definitely improve our squad. He has experience of big club football and also at international level.
"He can pass the ball well and he could be an important player for us in central midfield.
"Let's see how things progress. We're very hopeful."
Ahmadi was born in Enschede, but is of Moroccan descent and has played 10 times for Morocco.
He is known for his strong defensive qualities and could become Lambert's first major signing since replacing Alex McLeish as Villa manager last month.