Striker Holt was an integral part of Lambert's hugely successful three-year spell at Carrow Road, but the 31-year-old has been left disappointed by the club's refusal to offer him a new three-year contract and had a transfer request turned down last month.
But, while Lambert was fulsome in his praise for the centre-forward, he insisted he has not thought about signing Holt, and said: "I haven't even thought about that at all. Grant Holt was brilliant for me. In the three years I was there (at Norwich) he was a huge part of what happened at the club. He is a terrific guy and I have a lot of time for him."
He went on: "He was brilliant for me as a footballer and a captain but things move on and I need to know about Aston Villa Football Club before I do anything else.
"I will look at things here first and foremost. We will try to bring some guys in but I swear to God I haven't thought about that.
"I am really excited to be here but I haven't thought about anything like that."