The striker missed out on Sunday's win against Swansea because he recently went to see the outgoing manager to enquire about the possibility of leaving the Red Devils this summer
The Scot announced his retirement on Wednesday and rumours quickly surfaced that the striker had asked for a transfer two weeks previously.
Rooney was left out of the squad for United's 2-1 victory over Swansea on Sunday, and speaking to Sky Sports after bidding farewell to the club's fans at Old Trafford, Sir Alex confirmed that the former Everton man wants to leave the club this summer.
"I don't think Wayne was keen to play simply because he's asked for a transfer," he said. "I think he wants to think things through in his mind; I think that's a good idea.
"We're not going to let him go. I think he's maybe a bit frustrated that he's been taken off once or twice in the last few weeks."
And speaking to the BBC, he added: "We've refused [the transfer request] - he needs to go away and think about it."
Rooney was left out of the Champions League last 16 second-leg clash with Real Madrid, sparking rumours that he would be sold at the end of the season.
United, however, are keen to keep hold of the 27-year-old and were planning on offering him a new contract.
Sections of the Old Trafford support booed Rooney when he collected his Premier League winner's medal.