The 26-year-old's future is currently the subject of much speculation, with Roma believed to be open to offers for the Englishman in the current market.
According to The Telegraph, a number of clubs are keeping a close eye on Abraham's situation, with Tottenham among the teams expressing an interest on his signature.
Abraham was restricted to just 12 appearances during the 2023-24 campaign due to injury problems, only managing one goal and one assist.
However, the striker has scored 37 goals and registered 13 assists in 119 appearances for his Italian outfit since arriving from Chelsea in August 2021.
Abraham has a record of 26 goals and five assists in 89 Premier League outings during his career for both Chelsea and Swansea City.
Palace 'keen on Rochdale youngster'
Meanwhile, according to HITC, Crystal Palace are in the running to sign Rochdale teenager George Nevett during this summer's transfer window.
The 18-year-old is widely expected to leave Rochdale during the current market, with a number of clubs said to be keen to secure his services.
Palace are said to be looking to bring Nevett to Selhurst Park, but there is also thought to be interest from Southampton and Ipswich Town.
Nevett made 34 appearances for Rochdale during the 2023-24 campaign, having made the breakthrough into the first team from Rochdale Under-18s.
Blackburn Rovers, Queens Park Rangers and Millwall are also said to be keen on the centre-back, while a number of League One clubs are thought to have been tracking him this term.
Brighton 'in talks over new Gross deal'
Elsewhere, Brighton & Hove Albion are allegedly in discussions with Pascal Gross over a new contract.
The 32-year-old's future has recently been the subject of much speculation, with Eintracht Frankfurt said to be determined to sign him during the current transfer window.
However, according to The Athletic, Brighton are currently in talks with Gross over a new deal.
The report claims that the Seagulls are hopeful of convincing the attacker to extend his contract beyond the end of the 2024-25 campaign despite interest from the Bundesliga.
Gross, who is currently with the Germany squad at Euro 2024, was in impressive form at club level during the 2023-24 campaign, scoring five goals and registering 13 assists in 47 appearances in all competitions.
The attacker made the move to Brighton from FC Ingolstadt 04 in 2017, and he has represented the Seagulls on 261 occasions, scoring 32 goals and registering 52 assists in the process.