Manchester United appear unwilling to pay Leicester City the £85 million that they are demanding for centre-back Harry Maguire, and are considering Benoit Badiashile from Monaco if the deal falls through, according to L'Equipe.
Since his appointment, new boss Solskjaer have tried pairs of Jones, Smalling and Lindelof but also faced the same heat and thus has made it a priority again to add a central defender who can slot straight into his starting line-up next season.
Pogba started on the bench when United took on Perth Glory in a friendly on Saturday.
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Last season ended with just two wins from the final 12 games and Solskjaer is keen to get off to a flying start when the new campaign kicks off against Chelsea on August 11.
Lukaku missed training in Perth on Thursday evening and instead took partin a gym session.
Asked if the World Cup victor was a candidate to wear the armband, following United's first pre season match, Solskjaer said, "Yep.
We'll probably see them on Wednesday, I reckon", Solskjaer said to MUTV. "That's important over the next few weeks to get that link up over the next few weeks to get the best out of them and the best out of me".
United, in their new gold away strip, controlled a subdued first half with speedy winger Daniel James eye-catching on the left flank.