Hazard, a Belgium international, is one of the most highly-rated young players in Europe, and has alerted some of the biggest clubs on the continent by announcing his intention to leave the French champions for a greater stage in the summer.
Real Madrid, Chelsea and Arsenal are among the clubs to have been linked with the left-sided forward, but the player himself recently admitted an interest in joining Spurs - and Redknapp has now confirmed he and club chairman Daniel Levy are looking closely at the £30 million-rated player.
"Hazard is a player that we have spoken about," Redknapp said. "He is a player who is definitely on our list."
France Football have reported that Hazard has already agreed personal terms with the White Hart Lane club, although concluding a deal could be complicated by the current uncertainty surrounding Redknapp's future - with the former West Ham and Portsmouth manager strongly tipped to take over as England manager before the start of next season.
"Hazard is different class. He's still only 21 and has definitely got another few gears to go up. He's got the same attitude as Rooney at that age - he's fearless," Cole said recently. "He knows how good he is, and that's a positive. All the top players have got that belief and a bit of presence and arrogance, and he's like that.
"He's a bit like Messi. There's only one Messi and I don't want to put pressure on the kid, but he's like him - short, squat, powerful legs, great touch, he can finish, he's got everything."