The Brazilian has been part of the Reds' pre-season squad since the start of July but picked up an ankle injury during last week's training camp in Surrey, which led to him missing Saturday's 4-2 defeat to Queens Park Rangers in London.
"Unfortunately, it's worse news on Alex Telles than we hoped for, his ankle injury is a little bit more severe than we hoped and he'll be out for a little spell at least, the whole of August I would think," Solskjaer told club media.
With Luke Shaw still on holiday after helping England reach the Euro 2020 final, Brandon Williams was given the nod to start at left-back at the weekend.
“That is football. We've got kids wanting to play of course. Brandon has done well in the left-back position," Solskjaer added.
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