The Blues have had two offers rejected by United already and are insistent he will not be sold.
"I don't want Chelsea to do it before we go there," Mourinho said following Chelsea's 2-1 defeat of Aston Villa.
"Everybody in the club, in the board, they agree with me. They share that opinion.
"I think this period, by the ethical point of view, is a period where we're going to be quiet."
The transfer window closes on 2 September, which will give Chelsea exactly a week to sign Rooney, who has two years left to run on his contract.
Demba Ba started in Chelsea's win versus Villa after Fernando Torres struggled against Hull at the weekend, while Romelu Lukaku, who excelled at West Brom last season, emerged as a substitute in both games.
There are alternative targets should a third bid fail, with Anzhi Makhachkala striker Samuel Eto'o, who played under Mourinho at Internazionale, reportedly one of them.
Speaking prior to the Villa clash, Mourinho said: "We have plans B and C. Don't ask me names because it's difficult to speak about players from other clubs."