The Spaniard emerged as one of European football’s top marksmen after completing a cut-price move to South Wales for the 2012/13 season, but a series of injuries limited his playing time last term.
Although still considered a talented forward, Swansea are rumoured to be looking at offloading the 28-year-old in the coming months after clinching free agent Bafetimbi Gomis to partner Wifried Bony.
Since his fitness concerns, teams such as Liverpool and Arsenal have cooled their interest in the silky star, opening the door for Palace.
Tony Pulis is keen to build on a miraculous opening to his time at Selhurst Park, in which he dragged the Eagles from the foot of the table to keep them from an immediate return to the Championship.
Their success was based on a tight defence, but now the former Stoke manager – who eyed Michu while with the Potters – wants more attacking flair in his ranks.
The Spain international fits his requirements, and Pulis is hopeful that he can lure him to south London.
Atletico Madrid and Napoli have been linked with him, but the most serious interest is understood to be coming from Michael Laudrup’s new team in Qatar, Lekhwiya.