The Red Devils are sixth in the Premier League with two matches of the 2018-19 campaign remaining, three points behind fourth-placed Chelsea with an inferior goal difference.
Solskjaer has been tipped to oversee a squad overhaul this summer, with a wide range of domestic and European targets mooted, after a disappointing season at Old Trafford.
It has been suggested that major signings might be difficult for the Red Devils to sanction without a seat at European football's top table, but the Norwegian coach is not considering such a scenario.
"I'll have a final say if a player comes in or goes out," Solskjaer said at a press conference on Friday.
"And we've got regular meetings. I'm happy with the way it's going and we're supposed to sign 250 players because you're all writing about players we should sign, so hopefully, we can get players in you have written about as well. So you never know.
"In the long-term planning, we have to think about [the Champions League]. We might be in the Champions League next year, we might not be and you'd be surprised how many agents have been touting their players.
"Not touting, that's not the best word, is it? Telling us their players, their clients would love to be a part of Man United in the future. And that's just the lure of Man United, they know, the potential and size of the club, they know in the end that we will get back to the good days.
"We're having a tough time at the moment, in the last few seasons, we've not gone up to the standards we expect but it's up to me and the club to change it as quickly as possible if it's a season without Champions League, who knows.
"But players still want to come to Man United and you wouldn't be surprised by the names that you get asked."
The United manager was speaking ahead of a crucial trip to Huddersfield in the Premier League on Sunday, which is a must-win game for his team to stay within touch of the final Champions League spot.
The Red Devils wrap up their season at home to Cardiff City on May 12 and beyond that, a number of current stars could be set for summer exits.
Antonio Valencia, Ander Herrera and Juan Mata are all approaching the final weeks of their current contracts, while Matteo Darmian and Marcos Rojo have been deemed surplus to requirements.
However, Solskjaer gave a diplomatic response when quizzed on the future of certain members of his squad, as he stated: "You learn about them every single day.
"You get positive and negative surprises all the time, so of course every day here is chance to be part of the rebuild of Man United, definitely."