Bellingham left the pitch in the 57th minute of Real's 4-0 win over Girona on Saturday, where the midfielder scored twice, and afterwards, the club said that he had been diagnosed with a high-grade sprain of his left ankle.
Rose, speaking ahead of Tuesday's last 16 first-leg game with Real, is not so confident that the Spanish club will be without the LaLiga top scorer in Germany.
"I don't believe he'll be out until he's not in the stadium tomorrow," Rose told a press conference on Monday.
"I know Jude, he will do everything to play the Champions League game. He might see other doctors today in order to be fit. I've read a lot but we'll see if he's here or not."
Rose knows all about the quality of Bellingham, who he coached at Borussia Dortmund during the 2021-22 season, but even he didn't expect to see him netting 16 league goals already this season, along with four in the Champions League.
"I think he's at the right club and he made the right move. It doesn't surprise me that he made such an impact," Rose said.
"But the fact that he scores so many goals came as a bit of a surprise. I had him for a year, he's a great guy and a great footballer with an unbelievable mentality.
"If he doesn't play, Brahim Diaz would certainly be an option. Maybe they will play in a 4-3-3 system with Joselu up front."
Real's win over surprise title challengers Girona saw them open up a five-point gap at the top of LaLiga, and Rose is well aware how dangerous of an opponent his side faces, with or without Bellingham.
"They're in good shape. They know what it means to play in this competition and win it, we have to concentrate on everyone, Brahim, Rodrygo, (Toni) Kroos, (Luka) Modric... They are all excellent. I could name others," Rose said.
"But we have a good squad, good players. We're going to give everything on the pitch and take our chances. We want to get a good result for this first leg, we want to be competitive with the ball, in possession.
"We are not afraid of anyone."
