The 22-year-old has been in scintillating form since he returned to Friuli following a loan spell at Lecce, and he has been the subject of heavy interest from top Italian sides recently.
Juventus were believed to be leading the chase for the highly rated Colombian, but it appears their Serie A rivals Napoli are looking to hijack the deal.
The Azzurri have done a lot of business with the Zebrette over the past few years, with Fabio Quagliarella, Gokhan Inler and Pablo Armero all arriving at Stadio San Paolo from Friuli.
Napoli officials hope that the excellent relationship with their Udinese counterparts will help them beat Juventus to the signature of Luis Muriel.
The Colombian has scored 8 goals in 17 Serie A matches for the Zebrette this term and he is predicted a bright future in the game.