The Eagles value the 28-year-old Denmark defender – who joined Palace from Lyon in 2020 for about £20m – at nearer to £40m.
Fulham have been looking to increase their defensive numbers after Tosin Adarabioyo joined Chelsea following the end of his contract and Tim Ream moved to Charlotte FC.
They had a bid rejected for Aston Villa defender Diego Carlos earlier this week but completed the signing of Jorge Cuenca from Villarreal.
Andersen spent the 2020-21 season on loan at Craven Cottage from Lyon.
He has made 111 appearances for Palace in all competitions.

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