Chelsea have already seen two bids for the United striker rejected, but Mourinho is not yet prepared to cut his losses and will continue his pursuit until the September 2 deadline.
Mourinho was asked the motivation behind a probable new bid, despite United insisting Rooney is not for sale. The Portuguese manager 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 the self-proclaimed "Special One", who was speaking ahead of Wednesday night's 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 fallback option if a move for Rooney is blocked again.
Mourinho, who has been linked with a move for the 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 sympathises with those managers calling for the transfer window to close before the Premier League season starts.
The subject again arose on Monday when Arsenal's bid for Newcastle United's Yohan Cabaye on the day of their match at Manchester City provoked Alan Pardew's ire.
"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.
Villa head to Chelsea earlier than planned owing to the London club's Uefa Super Cup commitments at the end of the month, buoyed by their 3-1 win at Arsenal.
Mourinho is wary of Villa following their success at Emirates Stadium, despite the fact Paul Lambert's side lost 8-0 at Stamford Bridge last season.
"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. They are a team with qualities to play away, to play the counterattack 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."
Follow us @SprtNationalUAE