Although the Premier League transfer window closed earlier this month, United are able to add Llorente to their squad because he is a free agent.
The Spanish striker left Tottenham when his contract expired at the end of last season.
But the 34-year-old frontman looks set to return to the Premier League with United, who are said to have offered him a two-year deal.
The Red Devils did not sign a new striker this summer despite selling Romelu Lukaku to Inter.
Ole Gunnar Solskjaer believes Llorente can offer his team a different option, even if he is unlikely to be first choice at Old Trafford.
United will be looking to make it seven points from a possible nine in 2019/20 when they face Crystal Palace on Saturday.
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