The 22-year-old joined the Serie A club from Deportivo Cali as a teenager in the summer of 2010 before enjoying loan spells at Lecce and Granada.
The Colombia international returned to the club for the start of this season and has gone on to score eight goals in 18 appearances so far this campaign.
His displays for Francesco Guidolin's side have attracted interest from a number of rival clubs, most notably Juventus and AC Milan.
Muriel insists he is not thinking about a move away at present, suggesting a summer transfer to a team where he may not be a regular starter could be detrimental to his career.
"I would have no problem in continuing my career here," he told Planeta Futbol. "I like the city, it's calm and I would be happy to stay.
"Some of those who have left Udinese at an early age have then struggled to get regular games, that's why I'd like another season here.
"I've heard the rumours about a transfer, but I'm calm. My agent will arrive in Udine on Sunday and we'll see what he says and what are the real options.
"For now I'm thinking about ending this season well, then I just hope that we take the best decision for my future."