Arsenal are expected to make additions over the course of the summer, but have not qualified for the Champions League and could yet miss out on the Europa League.
Arsenal registered an interest in the Aston Villa midfielder, but did not follow up that enquiry.
Despite spending a couple of seasons in the Championship, Grealish has always been hailed as one of English football's brightest talents, and his is a name that seems destined to dominate transfer headlines this summer, even if by default inspiring Villa's survival may have made his chances of a move to a top club more hard.
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.
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Grealish has helped Aston Villa secure another season of Premier League football, but he could now opt to leave Villa Park this summer.
But Arsenal's transfer budget is likely to be a huge obstacle in following the inquiry with any meaningful bid.
The 24-year-old was integral to their promotion to the Premier League last season and was, by far, their best player upon their return to the top-flight.
As reported by Sky Sports News, the Cherries will decide whether or not to pursue a legal case against Hawk-Eye with their statement issuing an apology after an error by Aston Villa's goalkeeper Orjan Nyland, who carried the ball over the line against Sheffield United in the first game back after lockdown was not detected by their goal-line technology system.
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United have made Jadon Sancho their priority and are growing increasingly confident a deal can be done with Borussia Dortmund. It is understood personal terms will not be an issue.
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.
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