Mignolet moved to Anfield from Sunderland last month and said he had spoken to manager Brendan Rodgers about his position in relation to Reina.
"He spoke to me about that," said the 25-year-old. "It's not really something that has to go outside of the club. Competition is going to be in every single club.
"There was big competition in Sunderland with Craig Gordon and Keiren Westwood, and with Belgium.
"Everywhere you go, especially when you go to a bigger club, there's going to be a fight for places. It's a challenge that will only make you stronger.
"In the games I will get a chance to show what I can do."
Mignolet spent three years with Sunderland and admitted it was a tough decision to leave the Stadium of Light.
"I had a very good three years there so I'm very pleased how it all went in the end," he said.
Meanwhile, fellow new signing Kolo Toure believes he can fill the sizeable shoes left by the retiring Jamie Carragher.
The Ivorian joined Liverpool on a free transfer from Manchester City and is determined to repay the faith shown in him by Rodgers.
"It is a big honour," he said. "To be chosen as Jamie Carragher's replacement is unbelievable.
"He has been a fantastic player for England and this football club, and is a great leader.
"It will not be easy but I will do my best."