Paul Pogba
Regardless of numerous players being linked with a move to United this summer, Paul Pogba has dominated the headlines, being tipped to complete a transfer to either Juventus or Real Madrid.
Solskjaer, on the other hand, has been adamant throughout that the French midfielder is not for sale.
In terms of personal achievements, the 2018/19 campaign was Pogba's best season thus far, scoring 15 goals and registering nine assists in all competitions.
With United's high asking price being the sticking point, the 26-year-old looks set for another season for the Red Devils.
Unlike previous campaign, Pogba would be deployed much deeper as a No. 6 in a two-man midfield pivot- a similar role he plays for the national side.
Scott McTominay
Once considered underqualified to play for Manchester United, Scott McTominay has made his way from the fringes to a prominent role in Solskjaer's starting lineups. The Scottish international, personally, had a strong finish to his season, contrasting to his team's fortunes.
Since his breakthrough into the first-team, McTominay, with his top performances, injected industry and purpose to United's midfield.
With the unlikely to buy a replacement for Ander Herrera in this window, much onus would be put on Scott to perform a combative role in the middle of the park for Red Devils.
Marcus Rashford
After wreaking havoc towards the start of Solskjaer's reign at United, Marcus Rashford, similar to his fellow squad members, tailed off towards the end of last season. Although, the youngster's dip in form was due to an ankle injury which he seemed to endure in order to feature for the Red Devils.
With Lukaku set to depart, the manager would be putting his bet on Rashford and Martial to do the bulk of scoring in the upcoming season. Also, Rashford has enjoyed a positive pre-season and looks at his sharpest level.
Jesse Lingard
In the previous term, Jesse Lingard was one of the players who was majorly criticised for his below-par performances. After a hectic World Cup campaign last summer, The English international was troubled with constant injury issues, stopping him from featuring consistently for United.
Lingard, who scored 13 goals in 2017/18 campaign, managed only seven last season.
Although, he has excelled in a central position which yielded his best personal season. Solskjaer is set to utilise the 26-year-old's energy and vibrancy in a number ten role to execute a high press system.
Daniel James
Daniel James, United's first summer signing, has impressed the manager and supporters with the industrious shifts he puts in every game.
The Welsh winger is miles away from being a finished article and needs to improve various aspects of his play. However, the 21-year-old's energy and vibrancy could hand him a first-team role sooner than expected.
Often, Solskjaer has stressed on United DNA and talks about exciting the fans at Old Trafford.
James' pace and dribbling could tempt Solskjaer to start the winger in a handful of games next season.
Also, Juan Mata's lack of pace could push him behind the Welsh winger in the pecking order with manager seeking an energetic high press style of football.