Nubel has been a key player for the Royal Blues this season, with the shot-stopper recording a save percentage of 61.8% and, if he were to move to Bayern, he would follow in the footsteps of Manuel Neuer, who left Schalke to join the Bundesliga champions in 2011.
The 22-year-old's impressive displays have seen the German oust Ralf Fahrmann from the number one position at the club, as well as reportedly attracting the attention of Bayern.
Current Bayern keeper Ulreich, who replaced Neuer for large parts of last season due to the Germany international's lengthy absence due to injury, has urged Nubel to think twice about moving clubs, telling Sport Bild: “At 22 years old, I don't think he wants to sit behind Manu on the bench.
“I think if he comes, he wants to play.
“That's why in my view it makes no sense, Manuel has a contract and is absolutely undisputed.
"I also do not think that Alexander Nubel wants to come here as the number two, if he can play at Schalke."
Ulreich will start for Bayern in their DFB Pokal semi-final match with Werder Bremen on Wednesday night, while Neuer sits out with a hamstring injury.
Neuer is the current undisputed number one at Bayern, with the 33-year-old only being replaced when injured or being given a rest.
Nubel, meanwhile, is currently under contract at Schalke until 2020, but a bid from the Bavarian giants and a chance to learn under Neuer could be enough to lure him away from the Veltins Arena.
Schalke currently sit 15th in the Bundesliga standings and are only six points above Stuttgart, who are in the relegation play-off place with just four games left to play.
Bayern are aiming to make it a record-setting seven straight Bundesliga titles and hold a one-point lead over second-placed Borussia Dortmund.