Rooney is at the centre of a row between Chelsea and United over a bid made for the player which was rejected by the Premier League champions.
Mourinho was low-key when commenting on the offer in Bangkok, despite United provoking the Blues' ire.
Chelsea confirmed they want to buy Rooney, who is in dispute with United over comments made by manager David Moyes when he spoke to journalists in Bangkok last week.
Speaking in Bangkok following the first match of his second spell in charge - a 1-0 win over Singha All-Stars - Mourinho declined the opportunity to fuel the argument.
"I think that this situation is clear - nothing is a secret anymore," he said.
"The official bid is just about a certain amount of money and doesn't involve players. We want the player. We made the bid and now we have nothing more to say. Now it's up to Manchester United."
Asked if Chelsea had made any other bids, Mourinho said: "No, and we won't."
Asked whether it is now "Rooney or bust", Mourinho said: "yes."