The Norwegian is only guaranteed to be in charge until the end of the season but is still having a big input on contract renewals.
The likes of Juan Mata and Ander Herrera are out of contract this summer.
But The Sun claim Solskjaer has been asked to give his opinion on whether they should be offered new deals.
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The likes of Phil Jones and Antonio Valencia are also in the same predicament and face an uncertain future at Old Trafford.
Andreas Pereira is perhaps the player Solskjaer will have the most say on.
The 23-year-old has failed to impress on sporadic appearances this season and spent last campaign on loan at La Liga side Valencia.
Pereira could choose to walk away from United depending on how much he plays between now and the end of the season.
United have only recently triggered a 12-month extension in David De Gea’s contract.
And the reports claim Solskjaer is on the charm offensive to get the goalkeeper to commit to the club long-term.
De Gea is wanted by both Paris Saint-Germain and Juventus and it is believed the Spaniard would have definitely left had Mourinho stayed at Old Trafford.
Solskjaer has started his tenure in charge at United in superb style, winning all five of his matches.
The free-flowing, attacking style of football has also returned following the sacking of Jose Mourinho.
United are currently enjoying a break in Dubai as they have a rare week off before their next match.
It will be Solskjaer’s toughest test to date as the Red Devils take on Tottenham in the Premier League on Monday.
United currently sit sixth, six points behind Chelsea who occupy the last Champions League qualifying place at present.