Canaries boss Chris Hughton is keen to remould his forward line and help support club captain Grant Holt, who has scored just five goals this season.
Dutch striker Ricky van Wolfswinkel has already agreed a deal to move to Carrow Road from Sporting Lisbon in the summer.
Now it appears Hughton has turned his attentions to Murray, who is also attracting interest from Fulham following a fine season in south London.
Murray has smashed home 30 goals this campaign to help fire the Eagles into Championship promotion contention.
The former Brighton forward’s contract expires at the end of the next season and Palace have offered him a bumper new deal to secure his long-term future at Selhurst Park.
However, should Palace fail to gain promotion to the Premier League this season then reports on Thursday suggest both the Canaries and the Cottagers may make a move to sign the 29-year-old, who has never played in the Premier League.
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