The 22-year-old is likely to leave the Clarets following their relegation to the Championship, and according to 90min, the forward has interest from a number of Premier League clubs.
West Ham are thought to be well-placed to sign McNeil, but Newcastle United, Tottenham Hotspur, Everton, Brentford and Fulham have also allegedly asked about his availability this summer.
The Englishman found it difficult to make his mark for Burnley during the 2021-22 campaign, managing just one assist and zero goals in 38 Premier League appearances.
McNeil has shown that he can operate in England's top flight, though, and a number of clubs are seemingly keen to bring him back to the Premier League in the current market.
Meanwhile, according to Football Insider, Aston Villa are open to allowing John McGinn to leave the club during this summer's transfer window.
The Scotland international has previously been linked with Manchester United, while Tottenham are also believed to be admirers of the central midfielder.
The report claims that McGinn is 'far from an untouchable' at Villa Park, and Steven Gerrard's side would consider suitable offers for him during the current market.
Villa boss Gerrard is not believed to be 'totally convinced' by the Scot despite the fact that he made 35 Premier League appearances last season, contributing three goals and four assists in the process.
Elsewhere, Middlesbrough are believed to be keen to bring Crystal Palace goalkeeper Jack Butland to the Riverside Stadium during this summer's transfer window.
The 29-year-old made 15 appearances for the Eagles during the 2021-22 campaign, including nine outings in the Premier League, but the stopper's contract at Selhurst Park is due to expire next June.
According to The Sun, Boro are keen to bring Butland to the club this summer and are confident that Palace would be open to letting him leave, potentially on a season-long loan.
Birmingham City have also been credited with an interest in the stopper, but he is believed to be favouring a switch to Boro to play under Chris Wilder.
Meanwhile, according to The Sun, Burnley are keen to sign Jed Wallace on a free transfer this summer, with the attacker leaving Millwall at the end of his contract.
The 28-year-old scored six goals and registered 11 assists in 37 Championship appearances during the 2021-22 campaign, and a number of clubs are said to be competing for his signature.
The strongest interest is allegedly arriving from Burnley, though, with the club's new head coach Vincent Kompany viewing the attacker as an ideal signing in the current market.
West Bromwich Albion have also been credited with an interest in Wallace, who Burnley view as a potential replacement for McNeil, with the forward, as mentioned, potentially returning to the Premier League.
Kompany is also believed to be looking to take Taylor Harwood-Bellis on a season-long loan from his former club Man City.