Muriel says 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."