The Chelsea boss hung up his boots in 2004, the same summer the Swede joined.
Juventus signed the striker at the age of 22 from Ajax, and he spent two years there before heading for Inter Milan.
Last summer saw the pair move to England at the same time, with Zlatan Ibrahimovic now in the twilight of his playing career.
United will be hoping he can damage Chelsea and Conte's title charge at Old Trafford on Sunday (4pm).
Antonio Conte and Zlatan Ibrahimovic embraced one another when Juventus faced AC Milan in 2012
We must pay attention because, when he attacks the box, he's very dangerous
And Conte has urged his players to be on full alert around the 35-year-old – as he is still lethal.
“When Zlatan arrived at Juventus, I finished my career,” Conte said.
“It was a pity because I'd like to have played with him."
On his team facing Ibrahimovic, Conte warned: “We must have good defensive organisation, and we must pay attention because, when he attacks the box, he's very dangerous.
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"Also when he receives the ball, he's dangerous. He's a dangerous player.
"For this reason, I think my players must pay great attention and great concentration tomorrow to stop him, and not only one player, but the team.”
Ibrahimovic's future remains somewhat uncertain as he has not yet committed another season to United.
However, switching for Chelsea and finally working with Conte is not an option on the table.