Mourinho determined to land Rooney
Mourinho was asked the motivation behind a probable new bid, despite United insisting Rooney is not for sale, and the Portuguese said David Moyes could always reject any fresh approach, just as Chelsea had from Barcelona for David Luiz.
If Mourinho is feeling mischievous, the new bid could come prior to next Monday's Premier League trip to Old Trafford.
"You try, because nobody forbids you to try," said Mourinho, who was speaking ahead of the clash with Aston Villa.
"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 Luiz and Barcelona."
Mourinho has expressed satisfaction with his squad, which contains three strikers in Fernando Torres, Romelu Lukaku and Demba Ba, but also has a fall-back option if a move for Rooney is blocked again.
Mourinho, who has been linked with a move for Anzhi Makhachkala striker Samuel Eto'o, who played under him at Inter Milan, added: "We have plans B and C. Don't ask me names because it's difficult to speak about players from other clubs."
Despite hoping to remain active in it, Mourinho sympathizes 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.
"But at the same time it gives everybody a chance to be in the market while we are winning or losing points.
"We have conditions to try to improve our team by bringing in one more player and we are going to try that 'til the end."
And Mourinho is wary of Villa, following their success at the Emirates Stadium.
"It's not such a big surprise because Aston Villa can do that to any one of us," Mourinho said.
"Last season they had more points away from home than at Villa Park," he said. "They are a team with qualities to play away, to play the counter-attack game they played at the Emirates.
"They are a good team. It's not such a big drama, they can beat any one of the contenders."
Lampard had a penalty saved against Hull on Sunday but made amends by scoring with a free-kick in his first game of the new campaign.
For some time last season it appeared Chelsea were prepared to allow Lampard's contract to expire, before the club's record goalscorer agreed a one-year extension.
"I told him when I was not Chelsea manager and he didn't have a new contract, just by being a friend, I told him that I didn't see him playing for another English club and I wouldn't see him play in another small league, because of his nature," former Real Madrid boss Mourinho added.
"He demands a lot from himself. He wants to play at this level and I think he can."
Mourinho insists the use of the 35-year-old Lampard must now be managed, though.
"He is not 25 anymore, so the crazy Lamps that wants to play every minute of a Carling Cup match against a team from the Championship, the crazy Frank that wants to play and beat the record of appearances and play every minute every match is not here anymore," Mourinho said.
"Now it's about to keep his performance high for the most time we can, for the most seasons we can."