The Cottagers have already recruited one centre-back this summer, having signed Jorge Cuenca from La Liga side Villareal.
However, they are still keen to bring in another central defender after seeing Tosin Adarabioyo and Tim Ream depart this summer.
Marco Silva's side have identified Andersen as a potential target, but they were unsuccessful with their opening bid of £20m.
According to The Athletic, they have now returned to the negotiating table with an improved £25m proposal plus a further £5m in add-ons.
While Fulham will wait for an answer, there has been a suggestion that Palace have set the player's asking price in the region of £40m.
Andersen, who spent time on loan at Fulham in 2020-21, has made 112 competitive appearances for Palace since joining the club from Lyon in the summer of 2021.
Brentford making progress in O'Shea pursuit
Meanwhile, Fulham's West London rivals Brentford are reportedly close to sealing a deal to sign Burnley defender Dara O'Shea.
The Republic of Ireland international has been linked with a move away from Turf Moor following the club's relegation from the Premier League last season.
Scottish Premiership champions Celtic have shown an interest, while he has also caught the attention of several Premier League clubs.
According to The Telegraph, Brentford are leading the race to secure O'Shea's signature and closing in on a deal which would see Burnley make a profit on the £7m they paid to sign him from West Bromwich Albion last summer.
Despite being linked with a departure, O'Shea played a key role in Burnley's Championship opener against Luton Town, heading home his side's third goal in a commanding 4-1 victory at Kenilworth Road.
If everything goes according to plan, the centre-back will follow Igor Thiago and Fabio Carvalho in joining Thomas Frank's side this summer.
Palace considering Ayew bid
Elsewhere, newly-promoted Leicester City have submitted a £4m transfer bid for Crystal Palace forward Jordan Ayew.
The Foxes have made several additions during the course of the summer, having Facundo Buonanotte, Michael Golding, Caleb Okoli, Issahaku Fatawu and Bobby De Cordova-Reid.
Leicester are now looking to strengthen Steve Cooper's forward options and they appear to be pushing to sign Palace's Ayew.
According to journalist Sami Mokbel, Leicester have submitted a £4m proposal which is now being considered by Oliver Glasner's side.
The report claims that Leicester's offer is close to Palace's asking for a player who has entered the final 12 months of his contract.
The Ghana international has made 211 competitive appearances since joining the Eagles in 2018, scoring 23 goals and providing 22 assists.