Already missing six senior players, United lost Marouane Fellaini to suspension and Timothy Fosu-Mensah to injury during Thursday's 0-0 draw at Manchester City.
Their problems are particularly acute in central defence, with Chris Smalling, Phil Jones and Marcos Rojo sidelined, moving Mourinho to contemplate picking himself and untried 19-year-old Axel Tuanzebe.
"In this moment it's the only option we have: Axel, Eric (Bailly) and Daley (Blind)," Mourinho told reporters after the draw with City at the Etihad Stadium.
"I think Eric and Daley played absolutely amazing again. 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 option also. Mourinho and Tuanzebe against Swansea."
The draw at City, in which Fellaini was red-carded for headbutting Sergio Aguero, left United a point below their local rivals, who occupy the fourth and final Champions League qualifying spot.
World-record signing Paul Pogba was absent due to muscle fatigue and Mourinho said he would not return until the first leg of United's Europa League semi-final away to Celta Vigo next Thursday.
Mourinho has previously ruled out playing Wayne Rooney in midfield, but with Fellaini now banned and Juan Mata also on the treatment tables, he said he may have to reverse his decision.
"Yeah, it's an option. We don't have (other options)," he said.
"We have (Ander) Herrera and (Michael) Carrick and nothing else. And Timo Mensah, emergency like (against City) to help the team, strong legs, energy, but it's another one that we miss.
"So we are in trouble, but we fight. That's for sure."
United have allowed two central midfielders to leave the club this year, with Morgan Schneiderlin joining Everton and Bastian Schweinsteiger moving to Chicago Fire.
But Mourinho said United's predicament had more to do with bad luck than an errant transfer strategy, citing the knee ligament injuries sustained by Rojo and Zlatan Ibrahimovic in the same match.
"To have lots of players not playing is also something the players don't want," he said.
"We didn't tell Morgan, 'We want to sell you.' Morgan asked us, 'Please sell me. I want to go, I want to play every game.'
"So sometimes there's always this dilemma of (wanting to) keep a bigger squad, but the players don't want to stay. Even sometimes young players, when they are not playing, they ask to leave.
"So it's very hard and we arrive into an extreme situation. I think it must be unique in football – two cruciate ligaments in the same match.
"In my career, I had one cruciate (injury) in 17 years. And against Anderlecht, I have two in one match. We are very unlucky.
"The other small injuries, Pogba and Tony (Antonio) Valencia last week, are injuries of fatigue, the accumulation of matches, which is normal. Smalling and Jones was in the English national team training.
"So maybe it's a blessing. Maybe it's an opportunity to make the team stronger, make them become mentally stronger. So let's see if they can come back.
"I think the first one to be back is Mata, which gives us another option in attack. But in reality what we need now is one of the two central defenders (Smalling and Jones) to be back."