The Spaniard joined the European champions from West Ham in the summer on a free transfer and was immediately thrown into action.
Alisson picked up a calf injury against Norwich on the opening day of the season and Adrian has stepped up in his absence.
The 32-year-old has been in impressive form for the Reds, helping them to a perfect winning start to the season in the Premier League, but risks being relegated to the bench once the Brazilian is fully fit again.
However, Adrian argued in an interview with the Telegraph that Klopp can consider both of his options between the sticks as equals.
“When I signed for Liverpool I knew I was coming for a big challenge in my career and I think the competition makes us better,” he said.
“So to have two No.1s in the team is great for both of us.
"It’s a good decision for the manager because everyone wants to have the best and I think we are here - two No.1s.
“It’s not my mentality to be a No.2 and even less so when I am 32. Maybe in four, five years time I will tell you differently but it’s much better than being in a comfort zone of one No.1 and the other [goalkeeper] sitting on the bench forever.
"But I also like to be united and work together. I’m full of confidence to help Liverpool on the pitch and from the bench when the manager decides that Alisson plays.”
He added: “We will have a chat with the manager. Obviously he [Alisson] is fit and training with the team.
“As I say we are two No.1s now, waiting to see who is going to play. Last season Ali did really well and I’m here to push him and to help Liverpool.
“It will be the manager’s decision and after that we need to prepare for everything and if that is not in the Premier League [for me] it’s to try and have an opportunity in another competition.”
Adrian had several offers on the table when he departed West Ham, including proposals from Spain, Turkey, Saudi Arabia and Mexico.
But the goalkeeper’s hesitation proved to be worthwhile as the Reds came knocking.
“Inside of me was something telling me: ‘Wait because something good will come’,” he said.
“I think it was almost fate. I was close, very close [to signing elsewhere] but the moment I received the call from Liverpool I told my agent to stop all negotiations.”
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