The Blues had an opening offer for the wantaway striker immediately rejected last Tuesday and are expected to return with an improved bid.
And Mourinho suggested an over-long transfer saga could affect the "balance" of a team very close to the start of the season, or even after the new campaign has begun.
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"But, yes, he [Moyes] is right. The market is open until September 2 and many clubs are waiting to the last moment to make their decisions, and those decisions affect a number of other clubs.
"The one who sells has to go and buy, then they have to buy to replace, so no club is safe. Until the last minute, a club can go there and 'steal' a player. I don't mean steal a player, but steal the balance that a manager has when he's working with a team.
"In that aspect, we are OK because we don't have players to sell, so none of my players is leaving under any circumstances. Many teams will be under pressure until the last moment without knowing how the squad is going to be."
Mourinho, though, denies he is playing "mind games" with Moyes over Rooney, adding: "If to say my colleague in United is a great coach, deserves success, deserves time to work, didn't win trophies at Everton because it's difficult to win trophies there.
"If that is playing mind games, what would you say if I spoke bad about him? The best thing is not to speak, and if I don't speak."