The pair are two of Brendan Rodgers' four summer signings but more is expected of them than Celta Vigo forward Iago Aspas and Sevilla midfielder Luis Alberto.
Mignolet has the challenge of displacing Jose Reina, the long-time first choice, even if the suspicion remains he has been brought in as a replacement for the Spain international.
Toure has the unenviable task of filling the boots of the retired Jamie Carragher, although if Martin Skrtel remains at the club there is a chance his centre-back partnership with Daniel Agger may stand in the way.
However, neither player will shy away from the challenge of upsetting the established order.
"He (Rodgers) spoke to me about that (the Reina situation) but it is not really something which will go outside of the club," said Mignolet, who will get his first chance to impress in Saturday's friendly at Preston with Reina still on extended leave after Confederations Cup duty.
"Competition is going to be in every single club.
"I had competition back in Belgium with the local team, I had big competition at Sunderland where there was Craig Gordon, Keiren Westwood and other international goalkeepers and I had big competition with the Belgium national team so that's not going to change.
"Everywhere you go, especially when you go to a bigger club, there's always going to be a fight for places and definitely when you're a goalkeeper because only one can play.
"But it's a challenge. It can only make you better and make you stronger in the end.
"I can just do my best, train as well as I can, and in the games that I get a chance I will show what I'm worth.
"I'm not here to be sitting and resting. I'm here to come and progress, and play."
Toure's situation is slightly different in that he was released by Manchester City after a couple of years when he struggled to hold down a first-team place.
He intends to make up for that frustration with a new lease of life at Anfield.
"I wanted to join Liverpool because of course I want to play more games," he said.
"At City in the last two years, I haven't played a lot of games.
"Being there four years, two were very good and the last two years were much more difficult.
"The competition is tough, there are some good defenders here, we all need to fight for our place - I'm willing to do that."
Having been excluded from City's Champions League squad, last season Liverpool's absence from Europe's elite will not trouble Toure as much.
But he is keen to help the Reds regain their place in the top four.
"Last season I didn't play, I was out of the (Champions League) squad," he said.
"It has been a tough time but this season is going to be a great season for Liverpool.
"To be part of the team who can bring the club back to the Champions League would be amazing. That's what I'm looking for.
"I would like to be remembered as someone who did very well and that is why I am here.
"At the moment Liverpool are not in the top four but they have the history, the quality, the players and the mentality as well.
"This club is a winning club and I want to be part of history here, that's why I came - to try to build the team as far as we can, to be top four or to win a trophy.
"We just want to win trophies and want to play in the Champions League as well.
"There are a lot of good teams out there but with the squad we've got, we have great players and a great mentality here, we can do very well this season."