Kessie has enjoyed a fine season in Serie A with minnows Atalanta.
The Ivory Coast international is in demand having fired his current club up to sixth in the league table.
Chelsea have been linked with a January move, with boss Antonio Conte an admirer of Kessie.
Franck Kessie has opted to snub Man United and Chelsea for a move to Roma
Franck Kessie has been at the Africa Cup of Nations
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But Italian website Corriere dello Sport claim the midfielder is set to join Roma at the end of the season.
It is said the Italian giants have agreed a deal worth £20million plus add-ons – with two youth players set to move to Atalanta in return.
Franck Kessie has been in fine form for Atalanta this season
The 20-year-old is excited about a move to Roma, who are currently four points adrift of league leaders Juventus.
However, it could be a case of one in one out.