Speaking ahead of Chelsea's Wednesday night Barclays Premier League fixture at home to Aston Villa, Mourinho insisted the Blues are likely to test United's resolve again because "nobody forbids you to try".
The transfer window closes on 2 September and and the third offer could come prior to next Monday's trip to Old Trafford.
Rooney received a decent reception from United fans at Swansea
"You try, because nobody forbids you to try," said Mourinho. "When you think that you'd like to have one player and the market is open and the official bids are not forbidden, official bids are always accepted in an ethical way.
"Of course, the player's owners they can do exactly what we did in relation to David Luíz and Barcelona."
Barça have not returned with a second offer for the Brazilian defender, who was one of the major success stories of Rafael Benítez's six months in charge last season.
Mourinho, also linked with a move for Anzhi Makhachkala striker Samuel Eto'o, who played under him at Internazionale, added: "We have plans B and C. Don't ask me names because it's difficult to speak about players from other clubs."
Mourinho is keen to make at least one more signing this window
Despite hoping to remain active in it, Mourinho sympathises with those managers calling for the transfer window to close before the Premier League season starts.
"At a certain point I agree with what Alan was saying, that the transfer window goes too far, the transfer window goes to the third, fourth fixture of the season, which I also agree that is too much," Mourinho said.