United made a concerted bid for Bale in 2013 before the Wales international left Tottenham for the Spanish capital, and his struggles this term – coupled with the return of coach Zinedine Zidane – have led to reports that he could head for Old Trafford this summer.
But Bale’s agent, Jonathan Barnett, has insisted this week that his client wants to end his career with the 13-time European champions.
On Friday Solskjaer was asked about links to Bale and while he refused to be drawn on the winger specifically, United's caretaker manager insisted that the club will consider any player who will add something new to their squad.
“I can’t really comment on Gareth Bale or specific players because they’re property of other clubs but we should look for quality players, definitely, and players who could improve us as a team,” Solskjaer said.
“There’s so many factors you need to think about when you sign players. It’s easy when you’re in the media or when you’re a supporter, you can think short term. We’ve got to think about the longevity as well, who’s going to fit in personality-wise.
“So there’s so many things that we need to think about.”
And Solskjaer admits that he sees some parallels between the club’s 1999 treble-winning campaign and the current challenge as United make a tilt for the Champions League, FA Cup and a top-four Premier League finish.
“To win trophies you’ve got to win at least one or two really tough games. They’re like defining moments,” he said.
“We beat Liverpool, we beat Chelsea, we beat Arsenal back then [in 1999], and you think ‘We deserve a little bit of luck in the draw next time’ but Wolves away, what a difficult game that can be.
“So comparisons? Well we’re not challenging to win the league this year but we are challenging for the other two trophies.
“The more games you win, the more confidence you breed, the more hunger there is in the players. Every single game that you win puts another layer on that, on the way to becoming the team that we want to be.
"So I don’t agree with Gary Neville when he says that teams should go out of this and this to focus on that.”
United were paired with Barcelona in Friday’s Champions League quarter-final draw, and Solskjaer believes that the previous round’s away-goals win over Paris Saint-Germain showcased many of the qualities United will need to progress to the last four of the competition.
“I think we’ve shown against PSG that on any given day we can beat a top team. Then again there are so many variables and these games will be decided by margins," Solskjaer said.
“And of course that VAR, even though for me it’s a penalty, you can still be unlucky and not get it in the last minute and then we’d be out and no one would really remember the PSG performance.
“So yes, we can go all the way but you’ve got to be lucky and good along the way.”