Premiership big-spenders City have approached Eto'o, in a reported bid believed to be around £25million, but the Barca hitman does not seem to be lured.
"The player wants to stay and complete the last year of his contract," said agent Jose Maria Mesalles.
However, Mesalles conceded that Eto'o is ready to leave if Barca did not show willingness to keep him.
"If Barca don't want him they should say so, so we can pursue the player's future in a professional manner," he added.
"If they have a serious offer from Manchester City, and if they want to continue with this negotiation we could be interested.
"We haven't spoken to City but if Barca have reached an agreement it shouldn't be that difficult to reach a deal."
Eto'o was instrumental in Barca's treble victory last season as he hit 36 goals in all competitions for the Blaugrana.