Chelsea, since being bought by Roman Abramovich in 2003, have been ruthless with their firing of managers - namely the double sacking of Jose Mourinho, and Claudio Ranieri and Carlo Ancelotti getting the boot after less than two years.
However, Carragher feels that there are rumblings behind the scenes suggesting that Conte is not happy at Stamford Bridge following Chelsea's actions in the summer transfer window.
"I'd be very surprised if I'm sitting here in 12 months' time and he's the Chelsea manager", he said on Monday' during the first episode of The Debate on Sky Sports Premier League.
And after their defeat on penalties in the Community Shield, Carragher said he thinks it is unlikely that Conte will still be in charge next year.
Despite spending north of £140m this summer on Antonio Rudiger, Tiemoue Bakayoko and Alvaro Morata, the squad's size is still of concern, with only 23 players now available following the departure of Nemanja Matic.
"I think he's the type of manager who won't accept the involvement from people above, especially on the back of winning the title".
The Telegraph note that Danny Drinkwater, Ross Barkley, Antonio Candreva and Alex Oxlade-Chamberlain are all also on Chelsea's shortlist.
Meanwhile, he lost Nemanja Matic to a rival in United and has been so far unable to offload Diego Costa. They are bit like Real Madrid in this sense - they don't value the manager like other clubs, ' he continued.
"They've had a lot of distractions and I think they could have moved on from all of this if they signed an adequate replacement".
"They have a model where they have a big say over how that club is run; the owner, [technical director] Michael Emenalo and people involved there".
"Maybe that is a frustration for Conte".
And Conte wants more signings after 17 players left the club sine the end of last season. We don't know how good he is going to be, but that has been their business model going forward.
'The success they've had in changing managers ... they're not going to take anything off Conte. I would be very surprised if he's here in 12 months'.