Asked whether his players feel they can yet win the title for the first time since 2012-13 as clear-cut favourites have yet to emerge, Solskjaer added: "We can't get our heads too far ahead, but I am happy the players might be thinking that way because that means recovery, focus is better and those little margins mean a lot".
Six minutes after the break, it was 3-1, with a flowing move involving Pogba and Bruno Fernandes, and Rashford firing in his second. That win rate of 25 per cent is well above David Moyes (six per cent), but down on Mourinho (31 per cent) and Louis van Gaal (36 per cent) in the post-Ferguson years.
In total Rashford has scored 79 goals in 234 appearances for the Red Devil, since making his debut as a fresh-faced 18-year-old in 2016.
For the Red Devils, it would not be a big loss considering Solskjaer has not handed Lingard a league start in nearly a year. Whilst that is all good and well, it does not serve the team well and they keep asking for trouble.
Their expected goals against in league football under the Norwegian is 72.7, with their actual goals against tally at 67 (ignoring penalties and own goals), which is not a huge discrepancy.
Sterling's sweeping finish proved enough for City to return to winning ways at St Mary's Stadium as they became the first team to stop Southampton from scoring in the Premier League since the opening weekend of the season.
The hosts pushed for an equaliser, but Henderson did well to keep them out and United just about got over the line. The Red Devils constant and key problems at this moment of time, happens to be the side's lack of control against the teams weaker than them, and the amount of cheap goals that are being conceded. These two need to take control of the game, Fernandez needs to.
The persistent commentary on United is often reflective of the kaleidoscope of emotions through which this team take their fans over the course of 90 minutes: optimism routinely giving way to scepticism and back again, excitement tempered by despair. Ole Gunnar Salsakazar will have to find a way to play Pogba, Fernandez and Rashford Tojita, it's unbelievable how they didn't put them together.
Kevin De Bruyne set up that goal and now has 15 Premier League assists in 2020, which is three more than anyone else. Three of those have resulted in goals, behind only Jack Grealish (four) and Son Heung-min (nine).
Solskjaer's side now sit five points behind league leaders Liverpool but have a game-in-hand on the champions, and Scholes believes his former side can challenge in an unpredictable and competitive Premier League season.
Pose your questions now and The Athletic's Manchester United reporter Carl Anka will join in a couple of hours before kick-off.