Although the 31-year-old has spent much of the last two seasons sidelined through injury, his undeniable talent has given him the opportunity to once again prove his worth at the highest level.
Having said that, his mammoth wages are likely to have put off many potential suitors, and it looks as though the Red Devils decided early on that he didn’t fit in with their transfer structure.
Solskjaer hinted that could be the case as early as March of this year, with the club still pursuing Jadon Sancho after completing the signing of Donny van de Beek earlier this month.
The Norwegian said: “I can’t really comment on Gareth Bale or specific names because they’re property of other clubs.
“But we should look for quality players, definitely, and players who could improve us as a team.
"There’s so many factors you need to think about when you sign players.
“It’s not easy - I don’t know if it’s easy either - 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.”
Bale has been open about his love for Tottenham on a regular basis, and hinted that he would be pursuing a move back to the Premier League while on international duty with Wales earlier this season.
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In a chat with Sky Sports, he said: "If those options arise it is something I'd look at for sure.
"We'll see what happens, we have plenty of time in this transfer window and a couple of others as well. Time will tell but mainly I think the reason is that the decision is in Real Madrid's hands.
"I tried to leave last year but they blocked everything at the last second. It was a project I was excited for but it didn't materialise.
"There have been other instances where we have tried to go but the club won't allow it or they've done something. It's down to the club.”