United recently exercised their option to extend Pogba's deal at Old Trafford until 2022 but doubts over the Frenchman’s future remain.
Real Madrid and Juventus are believed to be keen in the midfielder, who has often spoke of his desire to play for the La Liga giants.
United are believed to be keen to keep Pogba, who they brought back to the club from Juventus in 2016 for a huge £89m.
Though ESPN claim Woodward and Solskjaer agree that the Red Devils should not be giving Pogba a bumper pay rise.
It’s reported that Pogba would be given a pay rise on his £270,000-a-week deal if he signs a new contract, though United will not be offering “extortionate” wages.
United finally saw Alexis Sanchez depart this summer with the Chilean’s contract having been worth around £400,000-a-week before bonuses.
And Woodward and Solskaer are in agreement regarding the wage structure at the club, insisting it will not be broken for any player.
ESPN add that United are relaxed over Pogba’s future and are open to allowing his deal to run into the final year if fresh terms cannot be agreed.
Pogba started on the bench as Manchester United beat PSG in the Champions League in midweek with the Red Devils now set to face Chelsea on Saturday.
Solskjaer said: “Of course, it’s very important, players if you lose games you’re determined to win, to bounce back I saw that focus at Newcastle and after you beat PSG gives you more belief and confidence.
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“Two very good performances and results but now it’s the next game and that’s what we’re focused on.
“[Chelsea’s start] is like many of us, some very good games, some lesser performances, football is just settling now and teams are just getting into their shape.
“We know it’s gonna be a tough game against Chelsea, we had maybe four or five games against them last year, two teams that know each other really well.”