Eto'o hit 36 goals in all competitions to inspire Barca's treble victory this term, and the Blaugrana chief will do his best to hold on to the 29-year-old.
"I would like to keep him, but he has a lot of offers and the market is very mobile," Laporta told reporters.
"We are very happy with him, it would be very beautiful if he were to finish his career with Barca."
Eto'o was close to leave Nou Camp when ex-boss Frank Rijkaard left last summer, but an impressive pre-season form prompted Josep Guardiola to keep him.
Meanwhile, reports emanating from England suggested that big spenders Manchester City are lining up a £20million for the services of Eto'o.
The explosive striker was also linked with AC Milan last season, as the latter are close to sell Kaka to Real Madrid for around €70million.