Bailly joined Man United on a four-year deal, subject to a work permit, on Wednesday.
But Mourinho isn’t said to be happy with just his acquisition and he has identified several other defenders as potential targets.
Real Madrid’s Raphael Varane and Athletic Bilbao Aymeric Laporte are on United’s radar, although Manchester City are also interested in the latter.
Everton’s John Stones, who Mourinho tried to sign while at Chelsea, is on the list, while Juventus’ Leonardo Bonucci, at 29, represents a more experienced option.
United enjoyed a formidable defensive record during the 2015/16 campaign but this was largely down to the excellent form of David de Gea rather than the defence.
Daley Blind lined up alongside Chris Smalling in central defence but it was clear that the Dutchman isn’t a natural defender. It is good that Mourinho has recognised the problem and is actively focused on solving it.