The 22-year-old has been a target for Mauricio Pochettino's side all summer, with the Argentine thought to be a keen admirer of the youngster's talent.
However, with just a day to go until the deadline he remains a Villa player, for now.
Grealish started in the 3-1 victory over Hull on Monday night, with Villa fans attempting to convince their academy star to stay by serenading him throughout the game with chants of "we want you to stay".
After the game, thought, manager Steve Bruce admitted that it was going to be a difficult task to keep hold of Grealish.
"He is a wonderful talent. We will do our best to keep hold of him, but it is going to be difficult," he admitted.
"We understand the human side. He will want to play in the Premier League, Europe, Champions League.
"The owner has made it clear that he wants him to stay. To be fair to Jack, he has got on with it."
It remains unclear as to whether the bid matches Villa's valuation of Grealish or not, but with the club looking to push through deals for the likes of John McGinn and Joe Bryan before the transfer deadline, they may have no option but to cash in on their prized asset.