Bayern was without Joshua Kimmich for Friday's shock Bundesliga defeat to Augsburg as he was forced to quarantine after coming into close contact with a positive case for coronavirus and has not been jabbed.
Serge Gnabry, Jamal Musiala, Eric-Maxim Choupo-Moting and Michael Cuisance are now also in quarantine having come into contact with a person who tested positive and has close contact to the team.
German media outlet Bild has since reported Bayern have told players they will have their pay withheld for time missed in quarantine if they have not been vaccinated, with claims saying certain members of the squad are considering legal action against such measures.
Head coach Nagelsmann does not foresee the issue causing a split in the team, though,
Speaking prior to Tuesday's Champions League clash with Dinamo Kiev, he said: "It's always a group's distinction that you don't always agree.
"In a functioning team, however, everyone has to be there for everyone. I don't think it will break the team, we have to grow from it.
"By not vaccinating, they are more likely to fail. But we have to be there for each other, we should grow from that.
"You often have conversations, if the person is positive, you have to be in quarantine as an unvaccinated person.
"The players are doing fine though, they are being tested. Josh could return earlier than the others because he was quarantined earlier."
Nagelsmann did, though, add that such matters should always be an internal matter and not be played out in the press.
"Of course I'm not happy that certain internals are leaked, that's not beneficial. It's also about private things," he added.
"There are too many things that are carried outwards. But that doesn't endanger our sporting success. It would be nicer if it was a little more closed.
"I have more fun when everything goes in the right direction. But we mustn't make the topic too big, every club has these problems. We mustn't project these issues too much onto the sporting side.
"We have moved forward in all statistical values. A week ago we were celebrated. Noise has been a part of FC Bayern for years."
The suspended Dayot Upamecano will miss out, while Kinglsey Coman and Marcel Sabitzer are injury doubts, but Niklas Sule and Josip Stanisic face late fitness tests having returned negative coronavirus tests after previously contracting the illness.
"We're still not sure if 'King' and 'Sabi' can play. With Sabi, it doesn't look too good because he has problems with his Achilles tendon and calf. 'King' no longer feels any muscle pain, but we have to see tomorrow," Nagelsmann said.
"We have an important game on Saturday, and we have to make sure he doesn't miss it. If they're both unavailable, we still have 13 outfield players.
"Despite being without at least eight players, we still have a very good team. 'Niki' [Sule] has tested negative and will be examined tomorrow. The same applies to Stanisic. We might have two more alternatives at the weekend."