Cissokho has joined Liverpool on a season-long loan from Valencia with Brendan Rodgers keen to add to his options at left-back.
Former Newcastle defender Enrique has no problem with Liverpool bringing in Cissokho and is determined to fight to keep his place in the side.
"I welcome the competition," Enrique told the club's official website. "If Liverpool sign another left-back then I understand it because it was just me here last season.
"Sometimes Glen Johnson had to play left-back. We need two players for every position, and I like it when I have competition.
"If you have somebody there who is really fighting for your position then it can bring more out of you because you know if you don't play well then you'll lose your place.
"Hopefully that helps me and I can play at my level as I did in the first six months when I first arrived at Liverpool."