The News of the World reported that Abramovich is furious with the unexciting way Mourinho's team are playing.
This is despite the Portuguese's promise in the off-season that Chelsea are set for a new attacking style.
On the other hand, Mourinho is angry that he was kept in the dark while the billionaire held talks with Ronaldinho's agents.
This is similar to their dispute last season, when Abramovich insisted on bringing Andriy Shevchenko from AC Milan against Mourinho's wishes.
A Chelsea source said: 'Roman came into the dressing room after the Portsmouth game, and you could see how upset he was.'
Chelsea narrowly beat Portsmouth 1-0 two weekends ago.
The source continued: 'Roman wanted Ronaldinho because that would have sent out the message to Jose about the way he wanted Chelsea to play.
'But Jose doesn't want Ronaldinho. He's not his kind of player, and he wouldn't have fitted in with his tactics.
'He's upset that Roman would approach Ronaldinho behind his back.'
Mourinho is furious that Abramovich was willing to splash out £100 million (S$300 million) in wages and transfer fee to land the Barcelona ace, after having to work within a limited transfer budget all summer.