Reports have recently suggested that Zinedine Zidane could replace Mourinho as United manager.
Carragher believes United could even decide to axe Mourinho at some point in this season.
“I’m not jumping to a knee-jerk reaction because Manchester United lost a game away from home,” he told Sky Sports.
“But after what’s happened in the summer, if performances like that continue, I don’t think Jose Mourinho will be the manager of Manchester United next sea-son – he may not be manager at some time this season.
“There will be coaches up and down the country looking at what Mourinho said in the summer about bringing players in, a centre-back. [Of the four they have] Jose has spent £30m on two of them and two are England internationals in Phil Jones and Chris Smalling.”