BRASILIA, June 11 (Reuters) - Brazilian state-run oil firm Petroleo Brasileiro SA has informed fuel distributor BR Distribuidora that it plans to sell its remaining 37.5% stake in the firm in a follow-on public offering, Petrobras said on Friday in a filing.

At Friday closing prices, the full Petrobras stake is worth 11.5 billion reais ($2.25 billion).

"This operation is in line with the optimization of the portfolio and the improvement of the company's capital allocation, aiming at generating value for its shareholders," Petrobras said.

BR Distribuidora SA is Brazil's leading fuel distribution company and was privatized almost two years ago through a share offering.

($1 = 5.1165 reais) (Reporting by Anthony Boadle and Tatiana Bautzer; Editing by Richard Pullin)