The Red Devils are preparing to face arch rivals Liverpool at Old Trafford this Saturday in what could be a crucial Premier League match.
At the moment, United sit second in the table with a two-point advantage over the Merseyside outfit.
Mourinho has previously criticised the lack of atmosphere at Old Trafford, and he did so again by suggesting that the travelling fans for Monday night's game against Crystal Palace should be given tickets for this weekend's action.
"I think [Liverpool and United] both want to finish top four but we both want to finish second, so I think it is a big game, and then Sevilla [in the Champions League] and Brighton [in the FA Cup], so we have three matches at Old Trafford," Mourinho told MUTV.
"If possible, [we should] give some tickets to the United fans that were [at Selhurst Park]."
United and Liverpool played out a goalless draw in the earlier fixture between the pair at Anfield.