The 31-year-old moved to the Etihad Stadium from Inter Milan last summer but started just four Premier League games under previous boss Roberto Mancini.
Mancini's successor, Manuel Pellegrini, has since told the former Cruzeiro star that he has no future at the club and left him out of the squad for their pre-season tour of South Africa.
Roma have moved quickly to try and land the experienced full-back and reportedly agreed a fee with City late on Sunday.
Maicon flew to Rome early on Monday to undergo a medical with the Giallorossi and a deal is expected to be completed within 24 hours.