Pogba has been in blistering form at Euro 2020 for France, as he was at the World Cup three years ago.
The France midfielder's future at United is in doubt as well, with the 28-year-old having just one year left on his deal at Old Trafford.
He has been linked with a move back to Juventus, in a potential swap deal with Cristiano Ronaldo, but the club want him to stay beyond next summer.
According to Champredictions News, they're willing to pay Pogba £400,000-a-week for five years, in order to keep him at the club, making him the highest-paid player in the country.
The reports says that the former United academy graduate is currently on £290,000-a-week, so this new deal would be a significant upgrade.
News say that Manchester City's Kevin de Bruyne was the highest-paid player in the Premier League last season, earning £385,000-a-week.
Pogba's United teammate David de Gea was second on the list, earning a reported £375,000-a-week, with Raheem Sterling's £300k-per-week rounding off the top three.
Technically last season Gareth Bale was the top earner in England's top tier, earning a reported £600,000-a-week, but Tottenham Hotspur only paid up to half of that, with parent club Real Madrid covering the rest.
United have recently been urged to sell Pogba this summer, rather than try to get him to sign a new deal, and sign jack Grealish replacement
The Aston Villa forward has also been targeted by Manchester City, according to recent reports, and was linked with United last summer, before signing an extension at Villa Park.
Solskjaer and Ed Woodward are still working on a deal to bring Jadon Sancho to the club, after failing to sign the Borussia Dortmund right winger a year ago.
The club have been linked with a centre back this summer to partner Harry Maguire, with Real Madrid pair Sergio Ramos, who has left the club already, and Raphael Varane both linked.
Atletico Madrid right back Kieran Trippier is also reportedly a target for Solskjaer, as he hopes to improve his side's attacking ability.