Paul Pogba's dispute with the United boss has been one of the most prominent storylines of the season so far, but the likes of Alexis Sanchez, Anthony Martial, Eric Bailly and Antonio Valencia are also understood to have had run-ins with Mourinho.
Keane infamously fell out with Sir Alex Ferguson during his time at Old Trafford and was soon sold by the club, but the former midfielder has taken the manager's side in the argument and urged the players to get over any personal disagreements.
"We talk about footballers and managers, not every player is going to get on with the manager, the manager is not going to like every player. But what you do as a footballer, and whatever disagreements I've had with one or two managers, when you cross that line, you play for your team," Keane told Notts TV.
"I don't care what fallout you've had with your manager, I don't care if you've been at each other's throats, because that is part of the industry, people do fall out. It happens in other industries, but unfortunately when you're Man United – one of the biggest clubs in the world – things will get exaggerated.
"But if you're a footballer for Manchester United and you put that jersey on and you walk out and you don't give 100% because you might be upset with somebody, then, no, good luck to Mourinho. I'm talking about players in general. Players who get upset with a manager, or a coaching staff, and think I'm not going to train properly because somebody upset me, there's a lot of crybabies out there, lots of crybabies.
"When you walk out on that pitch, you're playing for your pride, you're playing for your family, you're playing for your city, whatever it may be. Don't get that worried about what the manager said about you or the coaching staff. You get out there and play.
"You can fall out after the match, but when the game's going on, liven up, play with pride, play with energy, play with spirit. Hopefully play with a bit of a skill, but you can't always play with skill, you can have a bad day, but on your bad days you roll up your sleeves and you fight for that jersey and don't get distracted by the balloons out there."
United will look to end a four-match winless streak when they host Newcastle United at Old Trafford on Saturday.