Last week Mourinho said United had done well to complete 75 per cent of their transfer business before the new Premier League got underway.
The Special One went on to claim that he hopes his club can land one last new star before deadline day and wants another wide player.
Gareth Bale, Ivan Perisic and Christian Pulisic have all been linked with a move to Old Trafford in recent weeks.
And the Daily Mail say Bayern Munich star Robben is also be considered.
20. Bournemouth – 28,799 (v Man Utd, Dean Court, March 1957)
The ex-Chelsea star, who enjoyed great success with Mourinho at Stamford Bridge, is in the final year of his current contract at Bayern.
He is still regarded as one of the finest wingers in Europe despite his age and Mourinho remains a big fan of his.
The Daily Mail claim Bayern want a younger squad and Robben could soon be moved on.
And it is said the Dutchman could be tempted into joining United if Mourinho launches an offer this month.
United legend Gary Neville name-dropped Robben while calling upon his old club to sign a new winger as soon as possible.
Asked what business United need to do, Neville said: “I’d name a player similar to Arjen Robben – a wide player.
“[Marcus] Rashford did very well (against West Ham) but is he a wide player? Not really. I’m talking about someone who can generally play left side.
“If you could add one world-class winger to add to the squad you could say it was a complete squad…they are covered everywhere, they have such strength.”