The 18-year-old has been named in the Republic of Ireland's latest U21 squad for their final UEFA qualifier in Germany next week, although he is not expected to join the party while his future remains undecided.
The Birmingham-born midfielder, who is set to start in Villa's Capital One Cup clash at home to Leyton Orient on Wednesday, is still eligible to play for England and is considering his options.
Ireland legend Roy Keane is Lambert's assistant at Villa Park and the former Manchester United midfielder will be hoping Grealish stays with the national team.
Lambert said: "If he was Scottish I'd make sure to get him up to Scotland. I don't make rules or get involved so I'll leave it up to the lad himself, whatever he chooses I'll back it. He has to try to hang on to my squad in the first team.
"It's up to Jack what to do and to decide what country. He's done okay but has miles to go in the game.
"It is a great problem for him to have. I could be sitting here talking to you and saying I am releasing him. So I would rather have this kind of problem.
"It will be a long road to be a right top player, but at this minute in time he is doing alright."
Grealish spent the majority of last season on loan at Notts County and Lambert believes that has helped him mature.
The teenager came off the bench in Villa's opening day win against Stoke but was denied an appearance at home to Newcastle, when Lambert had to make a different substitution when Aly Cissokho suffered an ankle injury during the 0-0 draw.
"I was going to put him on on Saturday then Aly got hurt - but I don't have a problem throwing him in,” Lambert added.
"He's grown up in League One. That's a big thing, he's grown up in a man's environment."