The 18-year-old, who is the brother of Real Madrid star Jude Bellingham, made the move to the Stadium of Light from Birmingham City during the summer of 2023.
The attacker was a key player for the Black Cats during the 2023-24 campaign, making 47 appearances in all competitions, scoring seven times and contributing one assist.
There has been a host of speculation surrounding Bellingham's future in recent weeks, with a number of clubs believed to be interested in his signature.
According to the London Evening Standard, Palace are in talks with Sunderland over a move for the youngster during the summer market.
The report claims that the Eagles are firming up their plans for the transfer window and believe that Bellingham 'fits the profile' in terms of players they are looking to bring in.
Meanwhile, according to Football Insider, West Ham United defender Nayef Aguerd is set to leave the London Stadium during this summer's transfer window.
The report claims that the centre-back's exit is 'certain', with a number of clubs keen to secure his signature in the upcoming market.
A number of teams from Saudi Arabia are allegedly looking to sign him, but Lyon and Rennes are also in the hunt for the Morocco international heading towards the summer window.
West Ham are said to have placed a £35m valuation on Aguerd, and a deal could allegedly be completed in the early stages of the market.
The 28-year-old, who has another three years left to run on his contract with the Hammers, scored twice and provided one assist in 28 appearances for David Moyes's side during the 2023-24 campaign.
Aguerd made the move to the London Stadium from Rennes in July 2022, and he is seemingly set to leave the English club having made 58 appearances over the last two seasons.
Elsewhere, according to The Mirror, Aston Villa are exploring the possibility of signing English defender Archie Brown during this summer's transfer window.
The 22-year-old came through the youth system at Derby County before moving to Lausanne-Sport in Switzerland, and he then made the switch to Belgian giants Gent in August 2023.
Brown has made 41 appearances for his current side, and it is understood that his performances have drawn interest from the Premier League.
Villa are allegedly 'keeping tabs' on the defender, but Unai Emery's side are likely to face competition from Crystal Palace if they make a move for him.
Chelsea, Everton and West Ham are also among the clubs to be previously linked with the ex-Derby youngster.
Brown, who is believed to be valued at £17m by Gent, is expected to be on the move this summer despite having a contract with his Belgian club until the summer of 2027.