The 28-year-old spent the 2020-21 campaign on loan at Fulham from Lyon, making 31 appearances for the London club, before joining Palace on a permanent deal in July 2021.
The Denmark international has made 112 appearances for the Eagles, including their 2024-25 Premier League opener against Brentford last weekend, but the defender's time at Selhurst Park is allegedly coming to an end.
According to journalist David Ornstein, Fulham have reached an agreement with Palace over Andersen, with the two teams settling on a transfer fee of £30m, including add-ons.
The centre-back has entered the final two years of his contract at Palace, and he could soon be followed out of the door by Marc Guehi, with the England international being heavily linked with a switch to Newcastle United.
However, the Magpies are yet to come to an agreement with Palace over a fee for the 24-year-old.
Leverkusen 'exploring' move for Vermeeren
Meanwhile, according to transfer expert Fabrizio Romano, Bayer Leverkusen are interested in signing Atletico Madrid midfielder Arthur Vermeeren on an initial loan deal.
Atletico signed Vermeeren from Royal Antwerp in January, with the capital outfit believed to have beaten the likes of Arsenal and Manchester United to his signature.
However, the 19-year-old only made five appearances in the second half of the 2023-24 campaign, and there has been speculation surrounding his future this summer.
Romano claims that Leverkusen are keen on signing the Belgian during the current market, while RB Leipzig and Marseille are also keen to discuss a move with Atletico.
Diego Simeone's side are believed to be willing to let Vermeeren leave on loan this summer, as he is again likely to find it difficult to secure regular minutes during the current season.
Leeds 'confident' of keeping Gnonto
Elsewhere, Leeds United are reportedly confident that they will be able to keep hold of Wilfried Gnonto beyond the end of this summer's transfer window.
There has been a host of speculation surrounding the forward's future this summer, but according to Football Insider, Leeds are not under any pressure to sell him.
Having sanctioned the departures of Georginio Rutter, Archie Gray and Crysencio Summerville during the current window, Leeds are said to be in a position to keep hold of Gnonto.
The 20-year-old made the move to Elland Road from FC Zurich in 2022, and he has represented the Whites on 75 occasions, scoring 14 goals and registering seven assists in the process.
Gnonto has already played three times for Leeds this season, and he found the back of the net in his side's 2024-25 Championship opener against Portsmouth on August 10.