"It's very flattering being linked with the Motherwell job but I'm happy at Colchester and that's where my future lies," Lambert told the Daily Record.
"I love it down here and the club is fantastic. My chairman has been terrific with me and I'm excited about next season.
"Colchester is a great place to be and I'm loving every minute while I'm here. That's all I'm thinking about.
"I prefer being in England and gaining the experience down here. I had a terrific time of learning when I was at Wycombe and then, obviously, Colchester came along.
"I love being involved in the competitions down here and the club looks in a good position for the forthcoming season.
"I'm not interested in coming back to Scotland at the moment as we've a really good thing going here and League One is going to be extremely competitive.
"It is nice to have your name mentioned when good jobs come up but it's not for me."