The Eagles are going through a major squad rebuild this summer after releasing several senior players at the expiry of their contracts.
The club have already added quality to their ranks in Michael Olise and Marc Guehi, and they are now on the cusp of landing Andersen.
The Denmark international has been linked with several Premier League clubs over the past few weeks, including Tottenham Hotspur.
It is now reported that the former Fulham loanee has chosen to join the Eagles, and a permanent deal is close to being finalised.
Andersen was one of the stand-out performers for the Cottagers last term despite their disappointing relegation from the top-flight.
The 25-year-old made 31 appearances in the division last term. He showed his class with an average of 4.8 clearances and 3.2 aerial duels won.
He also produced key tackles and interceptions and now looks set to continue plying his trade in the Premier League with Palace.
The south London outfit will have a completely new-look central defence with Andersen potentially partnering Guehi next season.
Both players have come off positive loan stints. It remains to be seen whether they can form a solid partnership at the heart of the backline.
Patrick Vieira has the reputation of developing young players. The club will hope that the investment will boost their chances of finishing in the top half of the table.
They have managed to do so on only one occasion in the Premier League in 2014/15, where they finished 10th in the standings under Alan Pardew.
Stats from Transfermarkt.com and Whoscored.com