Chelsea have already seen two bids for the United striker rejected, but manager 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, 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 Barclays 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 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 fallback 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 sympathises with those managers calling for the transfer window to close before the Premier League season starts.
Source: PA
Source: PA