The Daily Star says Lambert played the youngest side his club have ever produced in the Premier League at Swansea earlier this week and knows he needs experience.
And a £10m move for Villa fan Lescott, 30, who has struggled to nail down a permanent place in City's side, could be a match made in heaven.
Lambert said: "He's been a top player and still is. I will sit down with the rest of the staff and we'll go through and see what I can do.
"I think everyone has said it's a really tough window in January. We won't just get people in for the sake of getting them in. There is ridiculous money and that sort of thing. That's not something I'll do but there's one or two that we will try for."