Fulham had been very interested in landing the Cameroon international, but could not agree terms with the Barcelona outfit.
Kameni's former team-mate, Ivan de la Pena, is now technical co-ordinator at Roma and he has seemingly played a part in the move.
Roma had been linked with Ajax's Maarten Stekelenburg, but they have instead opted for Kameni.
"His [Kameni] arrival is probable," sporting director Walter Sabatini said.
"That means it is something a bit more than just a possibility, even if anything can happen in the market.
"Stekelenburg? He is a great goalkeeper, but the decision was a technical one."
Roma are set to pay €3million for Kameni and have moved for him as Alexander Doni prepares to finalise his move to Liverpool.