Whereas The Red Devils, who defeated FC Rostov 1-0 in the UEFA Europa League on Thursday night, are looking to get their push for a top four finish back on track after falling six points adrift of Liverpool.
Middlesbrough caretaker manager Steve Agnew admits that Aitor Karanka's departure was "difficult and emotional".
Middlesbrough sit in 19th place in the Premier League table after failing to win any of their last 10 games.
"I'm capable of drip-feeding ideas into the group that will pay dividends", said Agnew.
"We did agree that change was required, we did accept that the team hasn't evolved since about Christmas and not only have we not gone forward, we've probably slipped backwards a bit", Gibson told The Times.
It is understood that Karanka, with whom Mourinho is still close, clashed with a number of Middlesbrough players, including Stewart Downing and Patrick Bamford.More news: Tillerson Makes First Diplomacy Trip To Asia
In the first year he arrived, the team was going into League One and he saved the team.
"I know people are cynical when you say that a decision was mutual, but he wasn't sacked". In the second year, he took them to Wembley to play in the play-off final.
Mourinho was asked if it had been a case of player power undoing the work of Karanka, in the same way that speculation has suggested Claudio Ranieri's Leicester reign was ended.
Super Sunday kicks off at the Riverside Stadium as Middlesbrough host Manchester United (12:00).
The former Republic of Ireland global continued: "There are names [being mentioned] galore, but I would personally go for Martin O'Neill, that would be my gut instinct".
Steve Agnew is now in charge until Middlesbrough appoint a new boss.