Allen, 28, joined Stoke in 2016 for £13m but, with the Potters preparing for life in the Championship, the midfielder is now on the hunt for pastures new and has attracted a number of Premier League clubs.
Now the Guardian are suggesting that Crystal Palace are prepared to enter the bidding war for the signature of the so-called 'Welsh Xavi' as Roy Hodgson looks to strengthen his Eagles side ahead of the new season.
With French midfielder Yohan Cabaye's future at Selhurst Park still uncertain, it is understood Palace are sounding out potential moves for a number of midfielders who could potentially replace him. Cabaye's contract is set to expire this summer and the former PSG and Newcastle man would reportedly need to take a wage cut in order to remain at the club.
The Guardian have also named Anderlecht midfielder Leander Dendoncker as a potential target for Palace should they allow Cabaye to leave the club.
Allen, who has played in the Premier League since winning promotion with Swansea City in 2011, could be interested in preserving his own top-flight status by making the move to London.
Were the midfielder to sign for Crystal Palace, he would be linking up with former Liverpool teammates Christian Benteke and Mamadou Sakho.