The Peruvian is out of contract in the summer and could spark a battle to lure him to either Emirates Stadium or Stamford Bridge, according to talkSPORT.
The report suggests the Bundesliga side are resigned to losing him for free after rejecting his wage demands and possibly leading to an offer from both Arsene Wenger and Andre Villas-Boas.
However, the Premier League sides could be scuppered by interest from the Russian Premier League, as their transfer window does not close until February 24 and talkSPORT claim there is interest from the east.
Zenit St Petersburg and Rubin Kazan are the two Russian clubs being linked and a transfer fee would likely be the prospect favoured by Schalke.
The 27-year-old moved to Germany from PSV Eindhoven after a highly fruitful four years with the Dutch giants.