The Sports radio station states that Swansea have made contact with Roma over Doumbia’s availability and are hoping to complete a deal early next week.
TalkSport go onto state that Swansea are willing to offer a fee of around £12m for the Ivory Coast international.
Fenerbahce are also interested in signing the 28-year-old according got Eurosport.
Doumbia spent the first half of the season on loan with CSKA Moscow, but the Russian club don’t want to make the move permanent.
Fenerbahce are on the lookout for a new striker following the departure of Moussa Sow over the summer. The Yellow Canaries have just two strikers in their squad.
Doumbia has five assists and 11 goals for CSKA Moscow this season.