The Red Devils were without a handful of first-teamers for Thursday's 0-0 draw at Manchester City and are stretched even thinner for Sunday's match after Maroune Fellaini was sent off for a senseless headbutt on Sergio Aguero and Tim Fosu-Mensah injured his calf after coming off the bench.
Paul Pogba, Juan Mata and Zlatan Ibrahimovic are all out but the problem is even more acute at the back, with Chris Smalling, Phil Jones and Marcos Rojo all sidelined.
That leaves 19-year-old Axel Tuanzebe next in line should Eric Bailly or Daley Blind need a rest, and Mourinho joked about an even more drastic decision.
"In this moment it's the only option we have: Axel, Eric and Daley. I have to speak with them and see how they are and how they feel. I'm also training hard in the gym so I can be an opton also," he said.
"Mourinho and Tuanzebe against Swansea."
The fixture list is not helping Mourinho manage his threadbare squad, with a Europa League semi-final against Celta Vigo on Thursday.
Read the full article on eurosport.co.uk: 'Mourinho and Tuanzebe at centre-back', jokes Manchester United boss