The Cameroon marksman, who has one year left on his contract with the European champions, is widely expected to leave Nou Camp this summer.
It was said earlier this month that Inter Milan are offering Eto'o an astronomical bid, and now big spenders City are also in the hunt for the 28-year-old.
"Eto'o has a stratospheric offer from City, which would convert him into the best paid player in the world," Laporta told Catalan radio station iCat FM.
Laporta confirmed that Eto'o wanted to see his current contact through, but admitted that the Spanish giants are likely to accept City's offer.
"It's starting to become clear that he has this monster offer. He wants to stay but an offer like this is very difficult to refuse," he said.
"If Eto'o accepts this stratospheric offer we will have to bring in someone."
The former Mallorca man hit 36 goals in all competitions for the Blaugrana last season to help them claim a magnificent treble.