Mutch has been at Selhurst Park for just under a year, having signed a four-and-half-year contract with Palace at the end of the January 2015 transfer window after leaving Queens Park Rangers, in a deal believed to be worth around £4.75million.
The former England Under-21 international has found first team opportunities limited this season and he has only made four substitute appearances in the Premier League, amassing to just 49 minutes of football.
He did start the recent 0-0 FA Cup third round draw with Bolton Wanderers but the midfielder is not in the plans of new manager Sam Allardyce, who succeeded the sacked Alan Pardew on December 23.
A host of Championship clubs are said to be showing an interest in the 25-year-old with his former employers Birmingham City, who he spent five years with, keen to tie up a deal.
However, it is high-flying Reading, who are third in the table, that have moved ahead in the race for Mutch's signature and manager Jaap Stam revealed towards the end of last month he is a target of his.