Villa's response followed comments by Carragher on the Stick to Football podcast where he told Villa supporters to "shut the fuck up" and said, "Aston Villa will never be Manchester United."
He also discussed speculation linking Villa manager Unai Emery with a move to United should the opportunity arise.
"Aston Villa will initiate legal action against Jamie Carragher for his unacceptable insults about the club and its fans," Villa chairman Nassef Sawiris said.
"Aston Villa will not allow anyone to stop our ascension in English and European football."
The club did not say on what legal basis it would take action. It did not immediately respond to a request for comment.
Carragher did not immediately respond to a request for comment on Villa's threat. He has sought to defuse the controversy, saying he made the remarks in jest.
"It was a joke after the stick Villa fans have given me over saying Emery may fancy joining Man Utd," Carragher said on social media.
"I hope these clown clips show me praising Emery/Villa like I have done for years & saying how pleased I was you won (the 2026 Europa League) in Istanbul."
He also reiterated that his comments reflected his high regard for Emery rather than any perceived shortcomings at Villa, saying he regarded the Spaniard as one of the best managers in the Premier League.