United have lost four of their last seven matches in all competitions
Already under scrutiny due to patchy performances before the international break, things went up a notch after Saturday’s desperate display at the King Power Stadium led to an embarrassing 4-2 loss.
Odds on Solskjaer being sacked were slashed after a fourth loss in seven matches in all competitions, yet it is understood he retains the backing of the Old Trafford hierarchy heading into a big few weeks.
Liverpool, Tottenham and Manchester City are United’s next three première ligue adversaires, while Atalanta arrive in a tough-looking Champions League group clash on Wednesday.
"Vous connaissez, we’ve progressed over the years – sixth the first when I was there for half a season, then third, second,” the United manager said. “You can see the progress, improvement, development and this season we still want to improve.
"Oui, we’ve signed some players that have raised expectations. Other teams have signed players and improved as well so we’re in the same boat as all the top teams. There’s pressure all the time.
“There’s pressure on me, bien sûr, but we’ve been through this before and we’ve come through it stronger as individuals and as a team.
“I’m just looking forward to the response now and I’m in dialogue with the club all the time, so that’s an open, honest discussion all the time.”
The pressure certainly seems to be more external than internal at the moment, with former Liverpool skipper Jamie Carragher taking aim at Solskjaer on Sky Sports.
The former defender spoke with Gary Neville about United and said they “need to have a better manager” at the end of the season if they are to compete with the Premier League’s best.
"Non, it doesn’t affect me,” Solskjaer said when asked about Carragher’s comments. “Of course you see some comments once in a while. I didn’t know what he was saying now.
“But of course we’ve got Liverpool on Sunday as well, so Jamie is always looking at all these little things. I’ve got my values, I’ve got my way of managing and I believe in myself.
“As long as the club believes in me, I’m pretty, pretty sure that Jamie Carragher’s opinion is not going to change that.”
Solskjaer was asked about a variety of issues at Tuesday’s press conference, with the United boss defending his “absolutely amazing” coaching staff and Cristiano Ronaldo’s tactical role.
The United boss also started his media duties by attempting to clear up his comments from Friday, when he said returning Marcus Rashford should “maybe prioritise his football and focus on football”.
Sat next to the forward at the training ground, Solskjaer a dit: “Just to get the elephant out of the room straightaway with, vous connaissez, the headlines that came after the chat I had before the Leicester game.
“Of course we’re so unbelievably proud by what Marcus has done on and off the pitch. And you know what I said and you made a headline out of one little comment that I never intended to be the focus of what I was saying.
“I was saying about Marcus and now it must be nice for the boy to focus on going into training, not feeling his ankle, or his shoulder, or his back. Now he can just go and enjoy his football and I think you all know that.”
Rashford scored shortly after his introduction as a substitute at the King Power Stadium and will be hoping to start against Atalanta on Wednesday and help United get out of this slump.
“Of course it’s not the gimmicky, jovial, happy camp,” Solskjaer added. “They’re focused and determined. As Marcus said earlier on, you look at yourself, ‘what can I do to help the team?»
“I’ve seen the reaction from the players and, vous connaissez, probably conceding four goals is a big eye opener for us, that we need to improve on different levels on loads of details.”