The News of the World says Abramovich is furious with the way Mourinho's team is playing, while the Portuguese is angry that the Russian billionaire held talks with Ronaldinho's representatives without informing him.
"He was promised it would be different this season but it's still the same old style.
"That's why he wanted to find out if he could really get Ronaldinho because that would have sent out the message to Jose about the way he wanted Chelsea to play.
"But Jose didn't want Ronaldinho. He's not his kind of player and he wouldn't have fitted in with the Chelsea pattern. He's also upset Roman would go behind his back when Jose had done everything to keep the peace this summer."
Mourinho is furious that Abramovich was willing to splash out £100 MILLION to land the Barcelona ace - after having to work to a limited transfer budget all summer.
Another source close to the Blues boss said: "Jose has always said Ronaldinho is a great player but that he's never really hurt Chelsea. In the games between Chelsea and Barcelona, he's had perhaps a 10-minute spell where he's been hard to handle but he wasn't consistently outstanding.
"Jose felt he'd have to completely reshape the team to even think of fitting Ronaldinho in - and that's not something he's prepared to do.
"He's done what the Chelsea board wanted him to do this summer by buying players within the budget but apparently that's not enough."