Napoli have shown the most interest in the Belgium international, who is understood to be valued at a reasonable £12m, but agent Nico Vaesen has warned the Italian outfit that they need to begin negotiations soon.
"Mignolet likes Napoli and the interest is not new," he told Radio Kiss Kiss. "Napoli have enquired about the player on several occasions now in previous transfer windows.
"There's no confirmation of a move to Napoli, though, and we'll have to wait to see if in the next few days they make an offer.
"Considering the market will close in a few days, I imagine they'll have to make a move soon if we want to continue the talks so that everyone can reach an agreement."
Barcelona are also said to be weighing up an offer for Mignolet to provide goalkeeping cover.