"Barcelona, wishes to... contribute to the effort to strengthen the bridges of peace and dialogue between the Israeli and Palestinian communities. The best way we can do this is with a ball," club president Sandro Rosell said.
Rosell made the announcement alongside Israeli President Shimon Peres during a visit to Tel Aviv the day after his club lost 2-0 at Italian side AC Milan in their Champions League last-16, first leg tie.
Israeli FA chairman Avi Luzon said the proposed game at the National Stadium in Tel Aviv on July 31 would be between Barcelona and a squad made up equally of Israeli and Palestinian players managed jointly by both of the national team coaches.
He added it was now up to Palestinian President Mahmoud Abbas to agree to the proposal. Rosell will meet Abbas on Friday in the West Bank town of Ramallah, the Palestinian seat of government.
Barcelona hosted a similar peace match at the Nou Camp stadium in 2005.
Even though they live side by side, Israeli and Palestinian teams do not play each other in competition, as Israel are members of UEFA and the Palestine soccer team play in Asia.
An issue that will have to be addressed for the match to go ahead successfully will be access to the Israeli stadium for Palestinian players and supporters as Israeli security policy largely bars Palestinians from entering Israel.
Rosell said Peres had undertaken to ensure that all players selected to participate would be permitted to attend.