The Eagles have already agreed to sell forward Oscar Cardozo to Fenerbahce and are actively searching for his replacement.
According to O Jogo, the Estadio da Luz outfit are keeping close tabs on Swedish forward Ola Toivonen, who has expressed a desire to leave his current employers.
The problem is Norwich are also keen on the 27-year-old despite already signing Ricky van Wolfswinkel and Gary Hooper.
Ola Toivonen has just one year left on his deal at Philips Stadium and is likely to be sold this summer with PSV looking to avoid losing him on a free transfer.
Even if he had arrived at the club as an out-and-out striker, Toivonen was mostly used as an attacking midfielder over the last couple of years, but he has, nonetheless, scored 60 goals in 125 Eredivisie appearances.