The 21-year-old was the subject of interest from Juventus earlier this month and, after scoring the only goal in his side's 1-0 win over Siena on Sunday, Muriel has admitted he would eventually like to move on to bigger and better things.
“I do hope to join a big club in the future,” Muriel told reporters. “I am working hard to achieve that goal.
Despite his desire to move on to pastures new eventually, Muriel was quick to point out that he still loves playing for Udinese, particularly as he gets to play alongside one of the club's greatest players of all-time.
He added: “Right now I am very fond of Udine and I love playing next to Antonio Di Natale – I learn a lot from him.
“I want to make the most of the opportunity I have right now.”
Having signed for Udinese in 2010, Muriel had loan spells at Granada in Spain and fellow Serie A side Lecce and then signed a new five-year contract in September 2012.
Muriel currently has one cap for the Colombia national side, having scored four goals in eight games for the Under-20s.