Jack Grealish is in demand with several Premier League clubs, including Arsenal, this summer.
Arsenal registered an interest in the Aston Villa midfielder, but did not follow up that enquiry.
Villa have made it clear that Grealish is not for sale and they would not be tempted to sell for anything under £80m.
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A number of clubs are willing to pay between £50m and £60m but Villa would not be interested in doing a deal at that level.
Arsenal's summer transfer budget has been hit by their failure to qualify for the Champions league and the ongoing financial uncertainty caused by the coronavirus pandemic.
Grealish has three years left on his contract and Villa want him to stay as they seek to establish themselves as a Premier League club.
Villa may have been forced to sell Grealish if they had been relegated but his goal in the 1-1 draw at West Ham on Sunday kept them in the Premier League.
He could be in contention for an England starting spot at next summer's European Championships if he continues to play every week, which is almost certain under Dean Smith.
But the 24-year-old, who was once a target for Mauricio Pochettino's Tottenham, has already admitted he may have played his last game at Villa Park.
It now looks unlikely Manchester United will try to sign Grealish in this transfer window, even though Ole Gunnar Solskjaer is a big admirer of the Aston Villa captain.
United have made Jadon Sancho their priority and are growing increasingly confident a deal can be done with Borussia Dortmund.
Discussions for Sancho centre around the transfer fee and structure of payments. It is understood personal terms will not be an issue.
Coupled with Villa's £80m asking price, there are doubts at Old Trafford about how Grealish would fit into the current Manchester United side.
Aston Villa boss Dean Smith joked Grealish's immediate plans are to get drunk, rather than discuss his future, as the club secured their Premier League status on Sunday.
Asked about Grealish's future, Smith said: "He goes out and gets drunk with me now!"
He later added: "We've got billionaire owners and he'd cost a lot, a lot of money."
The summer transfer window will run for 10 weeks from July 27 and close at 11pm on October 5.
A domestic-only window for trades between the Premier League and EFL then runs from October 5 and closes on Friday October 16 at 5pm. Follow all the news and analysis on Sky Sports News and across Sky Sports' digital platforms, including with our dedicated Transfer Centre blog.