Solskjaer was appointed Uniteds manager on a full-time basis on Thursday and the 46-year-old is looking to overhaul his squad in the summer after being promised a £250million warchest.
Borussia Dortmund and England wonderkid Jadon Sancho is at the top of Solskjaers wishlist and the Norwegian is also desperate to keep hold of his star players ahead of the 2019/20 campaign.
Uniteds owners believe the club can make a genuine assault on the title under Solskjaer next season and Pogba and Rashford are viewed as key figures going forward.
Pogba has been heavily linked with Zinedine Zidanes Madrid, while Barcelona are eyeing a move for Rashford as they search for Luis Suarezs long-term replacement.
Asked if the pair will realise all their ambitions at Old Trafford, Solskjaer replied: Thats our aim as a club to be achieving what we have done in the past and that is the expectations here.
And of course we are hoping to build a team strong enough worthy of the history of the club.
They are vital for our future.
You have got loads of players who you can build a team around and those [Pogba and Rashford] are two that you asked me about.
Rashford, who is tied into a contract until the summer of 2020Read More – Source