The 26-year-old has three international caps to his name, the last of which was handed to him in 2009, but Lambert suggests that he should be considered by manager Roy Hodgson after impressing at club level in the early stages of the season.
"I'm not going to tell Roy Hodgson how to do his job," ESPN quotes Lambert as saying. "That's his prerogative, to pick the national team. It's hard enough to pick any team.
"From my own point of view Gabby has been playing fantastically for me, he really has. To be fair to Gabby he hasn't let it bother him. He has just got on with it. You can't influence somebody to pick somebody, but for me and this football club, he's playing really well and long may that continue."
Villa will take on Newcastle United at Villa Park in the Premier League tomorrow.