Milan are expected to split from coach Stefano Pioli at the end of the season.
Talks with former Wolves and Spain manager Julen Lopetegui have been held, which has produced a backlash from Milan fans.
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Now Milan are turning to De Zerbi, says TMW, with talks planned in the coming weeks.
And key to the deal could be De Zerbi's ties with the Rossoneri, where he spent time as a youth teamer. Indeed, he said earlier this year: "It's not a normal club for me, I grew up in that club.
"For my life I will be grateful to this club."