Rooney has netted just three times in 24 appearances in all competitions this season with his only Premier League goal coming on the opening day of the season at Bournemouth.
The United captain did not look best pleased when he was surprisingly substituted in the second half of the Europa League win against Zorya last night.
And it raises doubts whether Rooney will be included in Mourinho's starting line-up for Sunday's crunch clash with Tottenham, who are six points clear of the Red Devils.
United have managed only 19 goals in 14 top flight games this season - fewer than West Brom and Crystal Palace - although they have found the net more regularly in the Europa League and League Cup.
Zlatan Ibrahimovic has 13 goals in all competitions but no other player has more than five.
"We are playing very well but goals make a huge difference and we are not scoring enough for the football we play, " Mourinho said.
"With me, he (Rooney) is an attacking player. In the national team, they can do with him what they want because he is their player, he is not my player. If they want to play him right-back, they can play him right-back. It's not my problem.
"In my team, he is an attacking player - he will play as a No 9 or a 10, or eventually coming from one of the sides.
"So, as an attacking player, normally he scores more goals. He has scored a couple, I think at Fenerbahce (in the Europa League) and one in the Premier League.
"We expect more goals from him, yes, but we expect more goals from everyone in the team.
"Maybe Zlatan is the one who is scoring but as the main striker it is normal that he has scored more goals. But we expect more goals from all the other attacking players."
Following six draws in their last eight Premier League games, Mourinho is demanding more from all his attacking players - and Rooney especially - to turn good performances into wins.
The Special One believes a win against Tottenham is vital for his side's chances of staying in touch with their title rivals.
Chelsea are currently 13 points clear at the top of the table as we enter the busy Christmas period.
Mourinho admits a win is vital on Sunday after four successive home League draws - against Stoke, Burnley, Arsenal and West Ham - yielded only three goals and four points.
"It is always important to win," he added. "When we played Arsenal, it was important to win. We played to win, we deserved to win, but we didn't win.
"We played against Everton, we had one point more than Everton. It was important to win and go to four points ahead of them. We played to win, we deserved to win, but we didn't win.
"Every game is important to win, so against Tottenham we are going to try to play. We are going to try and deserve (victory) and we are going to try to win."
