The Norwegian has spent £68million so far, on England Under-21 defender Aaron Wan-Bissaka and Wales winger Daniel James.
And the United boss is keen to continue strengthening as he looks to make his mark and overhaul a club that finished sixth in the Premier League last term.
Harry Maguire continues to lead a list of candidates as Solskjaer looks to strengthen in defence, while midfield has also been identified as another area for improvement – particularly if Paul Pogba departs.
Sporting Lisbon midfielder Bruno Fernandes and Newcastle’s Sean Longstaff both continue to be linked.
Asked about United’s summer business, Solskjaer told MUTV: “We are quite calm. We have been good in the market so far and we’re still working on a case or two.
“I have been in touch with Joel [Glazer, chairman], Ed [Woodward, executive vice-chairman] and the recruitment department over the summer. I’ve got to say it’s been very good so far.
“I’ve got the backing and we’ve got the people in we wanted to, for now, and there will probably be some more business being done.”
Solskjaer has also declared that £50million Wan-Bissaka and fellow new boy James both have the ‘X-factor’ – but has also asked for patience.
He said: “Both these players have the X-factor, real X-factors.
“They are great human beings who are hungry, hard working and just at the start of their careers.
“Of course we don’t expect them to set the world alight on the first day.
“But they are going to grow into big and very good players for Manchester United .”