Lambert, 42, is regarded as one of the brightest managerial prospects in British football after leading Norwich to back-to-back promotions before steering the Canaries to a 12th place Premier League finish.
However Lambert has reacted angrily to suggestions he was in the frame to replace Alex McLeish at Villa Park.
"Never once have I not felt wanted here," Lambert said on Sky Sports News.
"I have got a really great rapport with the fans here as everybody knows and it's a special thing I think with the fans and myself.
"I know how quickly that can turn if you are not getting results, but the three years I've been here.... the rapport I have with the fans is really special and a unique thing to get, and I love it here, I do."
Villa have also been linked with Wigan manager Roberto Martinez and former Manchester United striker Ole Gunnar Solskjaer, who has withdrawn his interest.
Source: AFP
Source: AFP