The London club began the journey home from Asia after Thursday's 8-1 pre-season win over Indonesia All Stars with no developments on their pursuit of Manchester United striker Rooney, for whom they had a bid rejected last week.
But Mourinho feels comfortable with his current options in his squad and has confirmed there has been no further bid for Rooney.
"At this moment we have made what you know; that bid which was public and official and after that nothing else," Mourinho said.
"But we are calm as we told you that we are calm because we are happy with what we have."
Mourinho was without six senior players for the tour to Bangkok, Kuala Lumpur and Jakarta who will join up with him for the first time in the next few days.
Spain trio Fernando Torres, Juan Mata and Cesar Azpilicueta, Nigeria's John Obi Mikel and Brazil duo David Luiz and Oscar had a break following the Confederations Cup and will now join the squad for four matches in the United States.
The pursuit of Rooney has led to speculation that Torres' place will be under threat but Mourinho wants the striker to relish any competition for places.