Mercedes have dominated F1 this season and the German team look certain to win the constructors' championship.
However, the manufacturer has been disrupted by a series of disputes between championship leader Rosberg and nearest rival Hamilton.
The situation came to a head at last weekend's Belgian Grand Prix when Rosberg collided with his team-mate on the second lap, ruining the Briton's race and ultimately costing Mercedes the chance of a one-two finish.
Webber, who was himself involved in a keen rivalry with Sebastian Vettel during his time at Red Bull, believes the pair are no longer listening to executive director Toto Wolff or non-executive chairman Niki Lauda and is unsure as to whether they can continue to drive in the same team.
"We have a very difficult situation at Mercedes where the drivers are not enjoying a good relationship," Webber told The Herald Sun.
"It's going to be interesting, not just for the rest of this year but can they drive together in the future? Is it okay for 2015 for the team to have the two guys together?
"The thing is, who is now going to try to put this back together? Is it the people who pay Niki's and Toto's wages?
"Because at the end of the day, if the drivers are not listening to these guys, do they have to say, 'Lewis and Nico, you go chat to the big guys at Mercedes, because they're paying you guys to get the job done in a team environment.'
"At the moment it's not a team, it looks like the drivers are doing their own thing."
Webber believes the situation means both drivers will not be able to fully focus on the next race at the Italian Grand Prix.
"The thing is for the drivers to stay focused on driving the cars now, because for them it's going to be a nightmare. The Thursday, the Friday, all the stuff out of the car, the media. This will just keep going up," he added.
"Let me tell you, when they get to the track, they'll only be thinking about each other. There's no-one else really in the race. They are really only focused on beating each other, and that's what happens when you have a car that is so dominant."