Solskjaer has brought in two new faces so far with the £50million capture of Aaron Wan-Bissaka from Crystal Palace and the £20m signing of Daniel James from Swansea.
He is thought to be targeting young British talent but insists nationality plays no part in the types of characters he wants to bring in.
Instead, the Norwegian claims he wants players who can make an immediate impact as he looks to improve a squad that struggled badly at times last season.
“It doesn’t matter if they are English, Norwegian, French, Brazilian,” he said. “You just want good players and good people.
“Quality and speed, of course, is a big thing in football nowadays. The more x-factors you have in a team, the better you are.”
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Solskjaer’s tactics rely heavily on speed and he has been busy trying to install his philosophies while the squad are on a pre-season tour in Australia.
Winger James is one of the fastest players in the country but is yet to be tested in the Premier League.
Asked if James was now the fastest player in the squad, Solskjaer replied: “Maybe Aaron Wan-Bissaka!
“The two of them do have top, top speed. Modern football is stop-start, it is go again, speed, tempo, quality.
“So those two have put their marker down. Of course, with our boys, we have got some quick ones.”
United will need to wrap up their summer business before the window shuts on August 8.
They are known to be looking for at least one centre-midfielder following the exit of Ander Herrera at the end of last month.