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The 22-year-old has also been nominated for the men's 2021 Ballon d'Or award, but Ibrahimovic said Mbappe needs to do more.
"I love Mbappe, but he isn't doing enough," Ibrahimovic told Telefoot. "He can become very strong if he hurts himself. He needs to taste blood and walk on fire.
"Surround yourself with people who tell you you're not good enough and you will become the best."
Ibrahimovic also said he has played a part in helping PSG attract some of the world's best players after enjoying a successful spell at the club from 2012 to 2016.
"When PSG were bought out, I was one of the first to be signed," he added. "And I'm very proud. Without me, PSG wouldn't have become what it is now.
"Some people think I came for the money, the city, the life. No -- I came, and everything changed."
Messi has endured a tough start to life in France because of injury problems and limped off at half-time during PSG's comeback win against champions Lille on Friday.
"It's a good challenge for Messi," he added. "He will try something new after a long period at Barcelona, and he's going to a very ambitious club that wants to win and is rising."