Blatter said after hosting the leaders of the Israeli and Palestinian football associations that they agreed to send delegates to a follow-up meeting this month to specify an "inventory" of problems between them.
The main issue is restricted movement into and out of the West Bank and Gaza for players and officials from Palestinian and visiting teams.
"As I am an optimist, at the end of the year we will have found a solution and will present the solution to the political authorities," said Blatter, who was told in July by Prime Minister Benjamin Netanyahu that national security was Israel's top priority.
"Security means also that there shall be solutions that people can come in and go out because Palestine has the right to play in FIFA competitions or Asian competitions," Blatter said.
FIFA task force
FIFA recognizes Palestine as a national team but Israel's denial of travel visas to players and officials forced the side to forfeit its place in qualification for the 2010 World Cup, and the issue flared again last month when teams from Iraq, Jordan and the United Arab Emirates struggled to arrive for a Palestinian-hosted youth tournament.
That impasse prompted Palestinian federation president Jibril Rajoub to demand that FIFA suspend the Israeli association and its teams from international football.
Rajoub and Israeli football president Avi Luzon spoke together for the first time Tuesday, Blatter said, acknowledging that the session at FIFA headquarters had a "lively" start.
"Both of the presidents wanted to express a little bit what they had on their heart," Blatter said. "I cannot say any more (about that), but at the end it was trust, confidence and football."
Neither Luzon nor Rajoub met with reporters after the session, leaving Blatter to represent the FIFA task force created for the issue.
It was attended by UEFA President Michel Platini, who includes Israel among his 54 member countries, Asian Football Confederation President Sheik Salman bin Ibrahim Al Khalifa of Bahrain and FIFA Vice President Prince Ali Bin Al Hussein of Jordan, which will host the next meeting of delegates in Amman.
Blatter said a report should be submitted to the FIFA executive committee meeting on October 3-4 in Zurich.
"We said football is connecting people and the solution would be one day that they play football together," Blatter said.