United have found it hard to establish any momentum in a challenging campaign that has threatened to spiral into disarray at times.
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They are six points adrift of the Premier League's top four but could still qualify for the Champions League through another route if they win the Europa League.
United face Club Brugge in the last 32 later this month, while their next FA Cup assignment is a fifth-round tie at second-tier Derby.
Despite distracting speculation about Ole Gunnar Solskjaer's future as manager, combined with fan protests against United's owners the Glazer family and the club's executive vice-chairman Ed Woodward, McTominay is adamant there is still a possibility of a happy ending for everyone at Old Trafford.
"It would be nice to come back and have a massive push with the rest of the boys to get into some finals, get some trophies under our belts and really set the bar for next season, set a bar that we don't step underneath," McTominay told United's website.
"All of the boys are fully focused on doing that and hopefully we can do it as well."
McTominay's performances have been one of the few bright spots for United this season, but the 23-year-old Scotland midfielder has been sidelined with a knee injury since late December.
He will be out until early March but has stepped up his recovery during United's warm-weather training camp in Spain.
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"It has been going well," he said. "Obviously, it is never nice watching football matches when you have been playing. You want to be involved and you want to be helping the team as well."
When he finally gets back on the pitch, McTominay will find United's new signing Bruno Fernandes adding his creative talents to the midfield, an ideal foil for the industrious Scot.
"In the brief moments that I have seen him in training, he has looked really good," McTominay said of the former Sporting Lisbon playmaker.
"He has looked like every type of player that the manager wants as well, so hopefully that can come to us on the pitch and he can show us what he can do. I can't wait to play alongside him."
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