The Belgium international completed his move from Sunderland on Tuesday night after putting pen to paper on a long-term contract, and he is set to battle against Reina and Brad Jones for a starting berth at Anfield
Reina has been closely linked with a return to old club Barcelona over the last few months, but the Spaniard insists he sees his future at Liverpool, while manager Brendan Rodgers has also stressed Mignolet has not been signed as a replacement for the 30-year-old.
Mignolet: "It's a challenge, but that's what you want.
"You want to play in the big games, you want to play for a big club and to play with pressure.
"I'm very confident in myself and my own abilities and I can't wait to get the first clean sheet under my belt.
"I've never been a nervous person. I'm quite confident in my own abilities.
"Competition can only be a good thing.
"I've been in big competitions wherever I've been - in Belgium with the national team and in Sunderland with Craig Gordon and Keiren Westwood, who are international goalies.
"Now it's the same again with Pepe and with Brad.
"It's only a good thing - to be competitive and to train as hard as you can, it can only bring the best out of you.
"Pepe is an experienced goalkeeper who has proven a lot over the years.
"I'm looking forward to working with him, the same as I am with Brad and the goalie coach.
"It's a big club and when you arrive it's a big thing.
"I'm very pleased to be here and I'm looking forward to getting started."