Manchester United have held informal talks with Southampton over the potential signing of defender Jose Fonte.
Sources told ESPN that Mourinho is keen to add to his defence before the transfer window shuts and is likely to table an official bid for the Portugal international later this week.
United have also made inquiries about Juventus centre-back Leonardo Bonucci, but are wary of more lengthy negotiations with the Italian club after finally completing the world-record signing of Paul Pogba earlier this week.
Rafael Varane was another transfer target for Mourinho, but the Frenchman is reported to have his heart set on staying and fighting for a place at Real Madrid.
As a result, United chiefs now consider Fonte to be the most realistic defensive target they can acquire before the transfer window closes.
The 32-year-old starred for Portugal in their victorious Euro 2016 campaign and made 37 league appearances for Southampton last season.
He was an unused substitute as Claude Puel's side played out a 1-1 draw against Watford on the opening day of the new season.
Earlier reports suggested that Mourinho was keen to sign a defensive leader in the mould of former United captain Nemanja Vidic to marshal the back four.
The Portuguese coach has already signed one defender this summer – Ivory Coast centre-back Eric Bailly, 22, from Villarreal for £30m ($39m).
Aside from wanting more experience in the back four, ESPN says Mourinho is also conscious of the fact that Bailly will be unavailable in January while he competes in the African Cup of Nations.
Southampton are reported to be open to the idea of selling Fonte and will not stand in the way of the defender should they receive a fee in the region of £8m.
United sold defenders Paddy McNair and Donald Love to Sunderland last week for a combined £5.5m.