The player was recently linked with a move to Aston Villa.
As per reports from Italy (translated by Sportwitness), Palace and Newcastle have joined the race as well.
Borini will be a free agent at the end of this season and it will be interesting to see where he ends up this summer.
The 29-year-old Italian has played in the Premier League before and he could be tempted to return if the offer is right.
However, it would be an underwhelming signing for Newcastle.
The Magpies need to bring in better quality players if they are to progress as a club.