McArthur only joined Palace last summer, but West Ham have reportedly been so impressed by his first season at Selhurst Park they have identified the Scotland international as a potential transfer target.
The Hammers apparently feel that he would bring energy and composure to their midfield ranks, as they look to bolster their options for next campaign.
West Ham have been frustrated with the way their form has tailed off this season and they are determined to strengthen to make sure that they have the strength in depth to last the distance next term.
McArthur's addition could be vital in this respect, especially with the future of Alex Song, who is currently on loan at the Boleyn Ground, still uncertain, but Palace are understandably keen to keep hold of him.
McArthur has been a key member of Palace's starting line-up this season, making 33 appearances for the Eagles, and it would be a major blow for them to lose him at a time when the club seem to be moving forward.
Alan Pardew has made an impressive start to life at Palace and the hope will be that they add players rather than lose key stars this summer.