"At the moment I can see everyone staying at the club because no deals have been done with anyone, I think", Solskjaer said.
"He has been injured lately so it was great to see him get 65-70 minutes tonight and he can only improve and I think he knows that himself".
"It's impossible to win the Premier League", he said.
United welcome PSG To Old Trafford on Tuesday 12th February in the first-leg of their blockbuster last-16 Champions League tie.
United's latest win saw them ease into the FA Cup fifth round with an impressive victory at Arsenal, courtesy of strikes by Alexis Sanchez, Jesse Lingard and Anthony Martial, but shot-stopper David de Gea believes that things can get even better at the club.More news: Jewish family says kicked off plane for 'religious reason' not body odor
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However, handed only a second start since Solskjaer took charge, Sanchez showed why he was once in such high demand as he latched onto Lukaku's pass before rounding Cech and finishing from a narrow angle for just his second goal of the season.
Despite starting his reign with eight straight wins, the 45-year-old is still in the dark about his future as United consider options including Tottenham's Mauricio Pochettino and Juventus coach Massimiliano Allegri.
They are playing with more confidence.
"Now, we're thinking about the next game which is Burnley". Arsenal will feel good about its chances here, looking to avoid a trip to United at all costs. Manchester United have consulted Ole Gunnar Solskjaer over the club's transfer plans.
"Also, we needed to change different players to play at centre-back".
"He knows that if they score one, we'll score two and he's always had that mindset".
"It's a win-win situation".
"Jonathan Wilson wrote a piece last week saying we sometimes forget that footballers are humans and that's true, particularly when they're underperforming". That winning run in all competitions has the team at the top of the league's five-game form table, but they still have a lot of work to do.