The £52m signing struggled to impress in his first season at United.
Nemanja Matic regularly kept Fred out of the starting XI under both Jose Mourinho and Solskjaer.
But the Brazilian looks set to stay at the club beyond next month’s transfer deadline, despite a number of loan enquiries being launched.
Fred has held multiple conversations with Solskjaer over the phone this summer.
And the Sun claim the United manager has reassured the midfielder that he will be given another crack to nail down a place in his first team plans.
An Old Trafford source told the publication: “Ole has held a couple of telephone conversations with Fred over the last few weeks.
“He wants to repay the managers faith.
“There has been some interest but everyone fully thinks he’ll come good.
“He’s been doing some private fitness work to help him get stronger, keeping to the schedule he was handed.”
Fred will finally join up with team-mates after taking an extended break in Brazil.
The former Shakhtar star has been celebrating his recent marriage in his home country.
But the 26-year-old is set to feature as United travel to Asia after leaving Perth in the coming days.
Before then, United take on Leeds in Perth.
Solskjaer is using the Australian friendlies as a chance to see which young stars can play a part in his senior side going forward.
Axel Tuanzebe impressed during Saturday’s win over Perth Glory.
And he is another player who looks to have a chance of joining Fred in the first team this term.
“Axel has a great chance of staying here and playing,” said Solskjaer.
“He has proved he can play at that level and has come back strong and focused.
“Of course there is a limit of players.
“Whoever performs will be part of the team and whoever doesn’t has to fight to get back in – but he’s one of the exciting players I can’t wait to see more of.”