The Red Devils have had a fairly quiet transfer window, with only Aaron Wan-Bissaka and Daniel James heading to Old Trafford.
Solskjaer is expected to spend again in the coming weeks after watching his Manchester United side finish sixth in the Premier League after a disastrous end to the season.
United finished a staggering 32 points behind champions Manchester City, with the Red Devils in need of a squad overhaul.
The Red Devils are in the hunt for a new centre-back and a central midfielder, with Leicester’s Harry Maguire topping their wishlist.
Newcastle’s Sean Longstaff and Bruno Fernandes of Sporting Lisbon are also midfield targets for United.
And while matching inflated price tags have been an issue for United this summer, Solskjaer is confident he’ll make a couple more signings.
When asked if he expects more changes to his squad before the start of the season, Solskjaer said: “It’s hard getting players in and over the line.
“We’ve been doing our jobs. We’ve been scouting, finding and identifying players.
“It took time with Aaron, it took time with Dan, but they got it over the line.
“It’s not like we’re going to sign 10 players. It can’t be a quick-fix.
“We’re working on one or two and we’re still hoping, but I also understand that the market has changed – prices have soared.
“There’s never any maximum, because there are players here that are coming into pre-season as well that are.
“I might just have a look at him again because if he has changed, as I think he has and it looks like, he might still have a career here.”
United are yet to meet Leicester’s world-record valuation of Maguire, with the Foxes demanding over £80m.
The Red Devils are closing in on the England international, who has told his Leicester team-mates he wants to leave.
United also have an issue with Newcastle’s valuation of Longstaff, with the Toon looking for £50m for the midfielder, despite him starting just eight Premier League games last season.
And Solskjaer admits United have to pay more to land their top targets due to the club’s wealth.
“We have been linked with so many players,” Solskjaer added when asked whether United have to pay a premium tax on players.
“I’m sure you don’t believe every single player that we’ve been linked with, but I think that Manchester United sometimes have, because of the wealth, maybe we have had to pay more, a bigger premium to get players in, and that’s just the world we live in.
“And we’ve taken our time, we’re not going to overpay, but we have to get the right people in, the right players.”