Lucas has recently been linked with a move to Inter Milan, but the former Reds stalwart turned TV pundit insists it would be bad for Liverpool.
"He's not just got to stay at the club, he's got to stay in the team," said Carragher.
"What he's giving this side now, they're getting victories on the back of it. He's totally different from Stevie Gerrard.
"Gerrard's a playmaker but he's a destructor, and that's what Liverpool needed. Results have improved massively since he's come in."