Reports over the last few days have suggested Villa are interested in signing Hoolahan and that the Republic of Ireland international is keen on a move.
Canaries chief executive David McNally emphasised on Wednesday on the Norfolk outfit's website that they had not received transfer requests from any of their squad members, adding that they had no intention of releasing any "senior players".
And on Thursday, Norwich boss Chris Hughton said Hoolahan was "very much a part" of the club and "as important as every other player" in the group.
Lambert managed the 31-year-old playmaker briefly when in charge of Livingston and then for three seasons at Norwich, prior to being appointed as Villa boss in 2012.
And asked about Hoolahan on Friday, Lambert said: "I had him for three years (at Norwich).
"I brought him to Scotland when I was up there, so I had known what he was like for years.
"When I was the manager of Norwich, he was fantastic, he really was - a big, big player.
"He was excellent. But he is Norwich's player, so there is no point in talking about him. I won't disrespect anybody on that front."
Talking more broadly about Villa's current transfer window efforts, Lambert indicated there had been little joy for the midlands club so far, but revealed Stephen Ireland could make his loan move to Stoke permanent.
Lambert said: "There are lads out there we have looked at and tried, but it just hasn't been possible. There is not really any great update.
"There are lads there we have identified that could bring experience to help the younger ones, but some you just can't do."
On Ireland, he added: "I think (Stoke) are trying to do something at the moment."
Lambert was speaking at his pre-match press conference for Monday's Barclays Premier League home clash with table-toppers Arsenal.
Villa, currently 11th, will assess the condition of defenders Ron Vlaar and Nathan Baker ahead of the match.
Both club captain Vlaar and Baker sat out last weekend's FA Cup third-round loss to Sheffield United with calf and hamstring problems respectively.
Forward Gabriel Agbonlahor, who also missed the cup tie, and goalkeeper Brad Guzan are fit despite having had niggles, but the game is too soon for midfielder Chris Herd and defender Joe Bennett to make their comebacks after injury.
Meanwhile, Lambert gave his reaction to former Villa midfielder Thomas Hitzlsperger publicly coming out as gay.
"I don't have an issue with that at all, I really don't," Lambert said.
"It's great that he has come out and said that about himself.
"It has happened in other sports and I don't have an issue with anything like that - if he can perform on the pitch, it doesn't matter.
"People in other sports have been applauded for (coming out), and with football, it should be no different."