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The Manchester United duo have been tipped to quit Old Trafford this summer and head to Spain.
Pogba has publicly discussed the idea of joining Real Madrid, with the France international claiming it would be a dream to head to the Bernabeu.
Rashford, meanwhile, is out of contract next summer – and Barcelona are tracking the England star.
Both Pogba and Rashford have been instrumental under Solskjaer, with the United duo a key part of the Norwegian landing the job full time.
And Solskjaer knows United cannot afford to lose their stars this summer if they are to challenge for the Premier League title next season.
When asked if both Pogba and Rashford can win the trophies they want to at United, Solskjaer said: “I would believe so.