The Red Devils are in seventh place in the Premier League table and six points behind Premier League leaders Manchester City and Arsenal.
The 20-time English champions have only collected four points from their last four Premier League games, losing to Pep Guardiola’s side and Watford.
Liverpool, on the other hand, can move level on points with title rivals City and Arsenal if the home side manage to end a two-game losing run against United at Anfield.
Former Reds defender Carragher pointed out that Mourinho will struggle to lead United to their first Premier League title in four seasons should the visitors leave Anfield pointless.
“I agree about United if they were to lose the game,” Carragher told Sky Sports.
“They haven’t had the toughest of starts, on paper, and up until now they’ve only played one so-called heavyweight who I think will challenge for the title – Manchester City – and they lost that at home.
“If you lose another one to another big title rival or top-four rival you start asking questions. It’s still early, but you could be eight or nine points behind.”
Liverpool are in fourth place in the Premier League table and three points adrift of City and Arsenal.
The Reds were 3-1 winners against United over two legs in the Europa League last 16 earlier this year.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news