The Red Devils are keen to sign both Everton defender Jarrad Branthwaite and Edmond Tapsoba of Bayer Leverkusen, says the Manchester Evening News.
United know that defensive issues from this season cannot be repeated next term.
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Raphael Varane and Jonny Evans could well leave in the summer, while Victor Lindelof is also a backup.
Branthwaite, 21, has impressed with the Toffees this season and is now in England reckoning.
Tapsoba, who is 25, has been a key figure in defense for Xabi Alonso's Bundesliga winners.