TalkSPORT says City's bid of £46m has met Milan's valuation for the Dutchman.
Reijnders, 26, has already agreed personal terms with City and is now due for a medical.
The Holland international was named Serie A Midfielder of the Year last season. Milan have become resigned to losing Reijnders this summer after a dismal past campaign which saw the club miss European competition.
Last term, Reijnders scored five goals and made five assists from 54 games in all competitions.