Cissokho had a spell at Liverpool on loan last season but failed to do enough to earn a permanent move to Anfield in the summer.
But having seen Lacazette coming through the ranks while he was at Lyon, Cissokho believes that the 23-year-old could make an impact at a top side in the Premier League.
He told footmercato.net: "It's great, I'm happy for him. He's a player who, when I was there, came from the reserve team to train with us, but you could see he had a future.
"He was serious in his work, and showed his determination in each session. He steadily grew in confidence, and has established himself in the team. I think he's starting to show his potential to the whole of Europe. He has quality, and is going to get better and better.
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Aly Cissokho has backed Alexandre Lacazette to succeed in the Premier League
We'll see what happens in the summer, but he easily has the quality to play in teams of that stature.
Aly Cissokho
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"What he is capable of doing now is very good for Lyon and France. He's a young player, and clubs like Arsenal and Liverpool have a lot of competition for places up front, and as a foreigner it's also different because you have to leave your home town and those close to you.
"It's a challenge, it's up to him to see if he's ready to take it on. We'll see what happens in the summer, but he easily has the quality to play in teams of that stature."
Lacazette is currently the top scorer in Ligue 1 this season with 17 goals, leading to speculation that the French international could be set for a move to the Premier League sooner rather than later.