Grealish, 19, has made three Premier League appearances from the Villa bench so far this season, reportedly catching Jose Mourinho's eye, though Lambert sees Villa as the best place for the teenager to progress as a player.
"This is the best place to be because he's getting the chance to get round and about our first team," The Guardian quote Lambert as saying.
"He's playing little bits here and there but he's still far from being an establish player. He's not near the finished article.
"But he's developing, which is great. The way his career is going hopefully something will be done."
Villa are said to be ready to offer Grealish fresh terms and a four-year contract.