Manchester United boss Solskjaer has helped Pereira rediscover his mojo in recent times, with the Brazil international previously struggling under Jose Mourinho.
The midfielder was a key part of the Red Devils side that rocked PSG 3-1 in the Champions League nearly two weeks ago.
However, his Manchester United future has been shrouded in uncertainty in recent times.
The player’s contract expires at the end of next season and, as of yet, no long-term extension has been forthcoming.
But The Sun claim Solskjaer has helped hatch a plan involving Pereira.
It is said the 46-year-old wants Pereira to sign a new four-year deal with United in the coming months.
And he then plans to send him on loan for next season to gain experience – but only if he pens the extension.
Leicester want the 23-year-old to sign on the dotted line.
And clubs from Spain and Italy also covet the signature of the United playmaker.
A United source is quoted as saying: ““The club are prepared to let him leave for a non-rival if it helps persuade him to stay long-term.
“Nobody wants him to go as he is well liked here and is extremely talented. We are confident he can make it here.
“We know he needs more regular starts though to take his game to the next level. He is highly valued.
“Ole is a fan of his but will struggle to find a proper role for him next season as things push on at the club.”
Meanwhile, the story on Pereira comes at a time where rumours of United’s transfer plans have been gathering pace.