United seem to be finding a groove and are now unbeaten in nine games in all competitions and within three points of fifth-placed Tottenham.
Although handicapped by a series of early draws, they improved their prospects with successive victories over Spurs and Crystal Palace and will make up further ground if they win at West Bromwich Albion on Saturday.
"Half-way through the race is not until Dec. 31, and I would say for the first half of the race it would be almost impossible to be in the top four," Mourinho told reporters on Friday.
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"But, one thing is to be 15 points from the top four, another is to be five points from the top four.
"What we have to try to do in these three remaining matches (in December) is be in a position that gives us a chance in the second part of the season.
"We are playing really well. If we can transform performances into results, we have a chance."
Zlatan Ibrahimovic has been in outstanding form and has scored eight goals in eight games, including the late winner at Crystal Palace on Wednesday.
"He is doing phenomenal," Mourinho said.
"Tomorrow is a last effort, then a week without football. They need it, especially him. In some positions you can protect yourself. As a striker it is impossible to hide."
After Saturday's game, United do not play again until Boxing Day, and have home matches that week against strugglers Sunderland and Middlesbrough.
Looking beyond that, Mourinho said he was not desperate to sign anyone in the January transfer window.
"I like my squad, I trust my squad," he said.
England defender Chris Smalling is back in contention for the first time since the end of October and although Eric Bailly cannot play against West Brom his injury is not serious.
United's manager also had words of support for British managers like Saturday's opposite number Tony Pulis, who he feels do not get the respect they deserve.
"If you manage big teams, you have targets impossible for Pulis, Pardew, Hughes, Moyes. British managers are not looked at like they should."
Pulis's Albion, the surprise team of the season, sit only one place behind United in seventh after Salomon Rondon's hat-trick of headers beat Swansea City in midweek.
"The group really like him (Rondon) because of the effort he puts in," Pulis said on Friday.
"You have to drag him in from training every day.
"United are on an unbeaten run and they deserve respect. I think they'll finish in the top four."
Former United defender Jonny Evans is an injury doubt.
(Reporting by Steve Tongue)
