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 Israeli Prime Minister Benjamin Netanyahu that national security was his country'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 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 Oct. 3-4 in Zurich.
"We said football is connecting people and the solution would be one day that they play football together," Blatter said.
Blatter was given a mandate in May from FIFA's 209 member federations, including the Palestinian body since 1998, to help improve conditions for football there.
"Palestine is recognized as a full member of FIFA but is not yet recognized as a full member of the United Nations," Blatter said, acknowledging the problems football's world governing body faced.
FIFA says it is currently investing $4.5 million in football development projects in the Palestinian territories, including a PFA headquarters in Al Ram. It previously helped fund upgrading the Faisal Al-Husseini International Stadium in Al-Ram, which staged the Palestine team's only competitive matches played at home: qualifiers for the 2014 World Cup and the 2012 Olympics.
The 150th-ranked Palestine team's next significant matches, when it needs players to travel freely, are in March at the 2014 AFC Challenge Cup in Maldives. The winner of the eight-nation tournament advances to the 2015 Asian Cup in Australia.
"This is what we want to solve. This is for next year," Blatter said.