The Portuguese coach witnessed his United defenders struggle against Chelsea's set pieces at Stamford Bridge yesterday.
United conceded via a header from Antonio Rudiger after Paul Pogba switched off at the vital moment allowing the German stole a march to score.
Mourinho wanted a central defender during the summer, but the message from the board was that there was not value for money in the market.
Mourinho spent the international break watching central defenders in person and was spotted at Serbia's game with Montenegro, in a baseball cap, as he sat next to legend Predrag Mijatovic.
He was reportedly scouting Fiorentina defender Nikola Milenkovic, 21, who he has been told will cost more than £40million.
Koulibaly, 27, agreed a new contract at Napoli in the summer but is understood to be open to making a switch to the Premier League according to the Sunday Times,.
Toby Alderweireld is also understood to be a target for United and Leicester defender Harry Maguire was also high on Mourinho's shopping list over the summer.
But Ed Woodward refused to sanction names who he deemed not good enough, which has created tension between manager and board as United lost to Brighton, Tottenham and West Ham in the Premier League and Derby County in the League Cup.
United almost scored their biggest win of the season on Saturday as they drew 2-2 with high-flying Chelsea at Stamford Bridge after Ross Barkley's last-minute equaliser.
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