Bove, 22, made 45 appearances for Roma during the 2023-24 campaign, scoring once and providing two assists, while he has another four years left to run on his contract.
There is currently a host of speculation surrounding the Italian's future, though, and according to HITC, Everton are one of the favourites to secure his signature this summer.
The report claims that Fulham, Leicester City and Bournemouth are also in the mix, with Roma believed to be willing to let him leave for around £18m during the summer market.
Bove came through the youth system at Roma, and he has represented his Italian side on 92 occasions in all competitions, but the midfielder is yet to be capped at senior level by Italy.
Southampton 'pushing to sign Downes this summer'
Southampton, meanwhile, are allegedly pressing ahead with their plans to sign West Ham United midfielder Flynn Downes on a permanent basis this summer.
The 25-year-old joined the Saints on loan from the Hammers last August, and he was in strong form during the 2023-24 campaign, managing two goals and three assists in 37 appearances.
According to GIVEMESPORT, Southampton, having secured a return to the Premier League for the 2024-25 campaign, are now pushing to bring in Downes on a permanent basis.
The report claims that Saints head coach Russell Martin is driving the interest, and there is hope that a deal can be secured before the club return for pre-season training next month.
A deal could allegedly be done for around £15m, with West Ham willing to let the midfielder leave this summer in order to boost their own budget for the summer transfer window.
Downes came through the youth system at Ipswich Town and then represented Swansea City ahead of a switch to West Ham in the summer of 2022.
Fulham 'offer Willian a new one-year contract'
Elsewhere, Fulham have reportedly offered experienced attacker Willian a new one-year contract.
The Brazilian was heavily linked with a departure last summer, with Manchester United thought to be keen, but he ultimately penned a fresh one-year deal with Marco Silva's side until June 2024.
Willian's contract is now due to expire once again, and it had been thought that Fulham had decided against making an attempt to convince him to stay for another season.
However, according to The Sun, the 35-year-old has been offered the opportunity to sign another one-year contract with his current club.
Willian was again a vital player for Fulham during the 2023-24 campaign, making 37 appearances in all competitions, scoring five times and registering two assists.
Meanwhile, the Brazilian has managed 10 goals and seven assists in 67 appearances for the London club since his arrival in September 2022.