The former Espanyol goalkeeper says the Gunners midfielder told him that he would like to move to the Catalan giants whilst they were on holiday together this summer
The Blaugrana have been strongly linked with a move for the Cameroon international following Seydou Keita's move to Chinese Super League side Dalian Aerbin earlier this summer.
Kameni believes the 24-year-old would be a smart acquisition for the Liga runners-up and revealed Song hopes to join Tito Vilanova's side.
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"[Song would] fit in at Barcelona," he continued. "He has all the features to play there. We all know what kind of player Barcelona like and he is one of them."
Kameni also spoke of his international team-mate's resemblance to one of Barcelona's former players, adding: "He is like Yaya Toure, but with much more mobility. He is very mobile but can also pass well. He is a complete player."
And he went on to comment on Song's rapid development in recent seasons, saying: "Alex has demonstrated how good he is during his time with Arsenal. He has always progressed well, but his last two years have been spectacular.
"He is a very focused kid, with his head in the right place. He always wants to improve and is willing to listen to others and work on his weaknesses.
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The player himself recently indicated that Barcelona had shown an interest in him, but denied that he wants to leave Arsenal for the Spanish giants.
Song joined Arsene Wenger's side from French team Bastia for €1.3 million [£1m] in 2005, and has gone on to make over 200 appearances for the club.