The France international, last year's player of the season in the Bundesliga, had been out since mid-November with an ankle injury but made his comeback in their win over VfL Wolfsburg on Saturday delivering one assist.
"Christo could only complete part of the training today because there was some reaction (from his injury)," Rose told a news conference. "We will certainly not start with him tomorrow.
"We will have to see if he can be with us tomorrow at all but we won't be taking any risks we have a lot more matches this season."
Leipzig will need to be working hard to get any possession against Manchester City one of the best teams in the world, Rose said, and must use their few chances against the English side.
City are desperate to do well in Europe this season, having never won Europe's elite club competition. They were knocked out by eventual champions Real Madrid in the semi-finals last season, having lost the final to Chelsea in 2021.
"They are one of the world's best teams. We are well prepared, have trust in the team and with the fans on our side we hope to play a good game," said Rose. "What's important is to have some possession and not just run after the ball.
"We have to have fun in shutting down spaces, defend against their positioning game. We have to have fun working as a block, we have to have fun in defending. When we win possession we have to use the chances that we get."
City had also faced Leipzig in the group stage of the last edition of the Champions League with each team winning their home game. The return leg is on March 14.
