German giants Bayern Munich are believed to be considering a move for Barcelona goalkeeper
Neuer was recently granted a short break
"Captain Neuer will instead take a short holiday after consulting the German record champions' medical unit," Bayern said in a statement on Friday.
"The 31-year-old will spend his time in warmer climes until 18 February. Neuer has been assigned individual training plans to continue his rehab on a daily basis."
The club are believed to have switched focus from Marc-Andre Ter Stegen to Cillessen, whom they scouted in a recent Copa del Rey fixture.
Ter Stegen is seen as very happy with his status at Barca, as well as his family life in Spain, and isn't considered to be a conceivable acquisition. Cillessen, however, could possibly leave the Camp Nou for pastures new.
Neuer, meanwhile, is hoping to return to action before the end of the season.
I'm not sure that Sven Ulreich is even playing. I have postulated a theory that Manuel Neuer's soul and consciousness takes over Sven at every game.— Scotticus (@FCBScott) February 10, 2018
"There is no specific date," he said last month. "We have to play it safe now and wait and see how my body handles the next few steps.
"But I am very optimistic and I know I will play in the second half of the season. I have to say I'm doing very well. I think my foot is doing very well too."