The 25-year-old sealed a switch from Sunderland on Tuesday, prompting further speculation that his Spanish rival is heading for the Anfield exit.
|10/1||Liverpool are 13/8 with Coral to finish in the top four next season
"I think who becomes the Liverpool No.1 is going to be Brendan Rodgers' decision," Gerrard told Sky Sports.
"I think he has gone on the record and said he wants to keep Pepe Reina, who is a world-class goalie - and Mignolet had a fantastic season as well so competition for places is going to be really healthy.
"It is going to be an interesting one, we are going to have to keep our eye on it.
"I know Pepe won't give up the No.1 without a fight. I have experienced him in top, top form and I think on his day he's in the top five keepers in the world so it's going to be an interesting one to keep the eye on."
Mignolet is Liverpool's fourth summer signing following the arrivals of Luis Alberto, Iago Aspas and Kolo Toure, while Goal exclusively revealed the club have made a move for Aston Villa striker Christian Benteke.