Blatter met with both associations, as well as Israeli and Palestinian political leaders, during a visit to the region in hopes of finding a way to ease the tension. FIFA is the international soccer governing body.
"Football has the power to connect people," Blatter said at a press conference last week in Jerusalem. "Football has the power to construct bridges. I am coming here and going to your neighbors ... to try to construct bridges and to try and make sure that football is not dividing, but football is uniting."
Instead of a vote, Blatter suggests a game between the two national teams, offering Zurich, Switzerland, as a possible location.
The Palestinian group objects to Israeli teams playing in the West Bank. They also say Israel restricts movements of Palestinian players between the West Bank and Gaza as well as for international matches.
"They keep bullying here and there, and I think they have no right to keep being the bully of the neighborhood," Palestinian Football Association President Jibril Rajoub said of Israel. "If the Israelis are using the issue of security, I can say that their security concern is mine. I am ready to fix parameters for security concerns, but security should not be used ... as a tool in order to keep this racist, apartheid policies."
He declared the situation in the West Bank far worse than apartheid that existed in South Africa because right-wingers and extremists in Israel want to "delete Palestine." In the 1960s, FIFA suspended South Africa for decades after it failed to comply with the association's nondiscrimination policies. The nation was also expelled from FIFA a month after the Soweto Youth Uprising of 1976
"I am not asking for the suspension of the Israeli association; I am asking to end the suffering of the Palestinian footballers," Rajoub said. "I am asking to end the grievances, the humiliation we are facing."
Israel Football Association President Ofer Eini said the restrictions on movement are a question of security. Eini said the association has no influence over such matters. He said the Palestinians are mixing sports and politics.
Association CEO Rotem Kemer said 95% of travel requests for players have been approved in 2015.
"We will continue helping the Palestinian association," Eini said. "We will extend a hand to them. If football is to be the unifying thing, I embrace them because I want football to flourish there just like I want it to flourish here."
While it may be true that 95% of permits have been approved this year, Susan Shalabi, director of the Palestine Football Association's international relations department, said even denying one permit can have a hugely detrimental effect on competition.
"So they say they've approved 95% of the permits. Let's be more optimistic and assume that they approve 99%. What's the point if the 1% includes the head coach, captain or goalkeeper of the national team? Or those of a visiting team? Will any association accept to play without all or any of these? It's about the principle, not statistics. Footballers should not be denied to move at all," Shalabi said.
Blatter said he is working to remove the suspension vote from the agenda. The vote would require 75% of FIFA's 209 member associations to succeed. Blatter said Israel has not violated any FIFA rules, and that other mechanisms exist to address issues between FIFA members, such as an ethics committee and a disciplinary committee, but he said FIFA rules allow the Palestinians to call for a vote.
The Palestinian bid to have Israel suspended from FIFA is part of much broader international pressure coming to bear on Israel to recognize a Palestinian state. The Vatican's recent recognition of Palestinian statehood
is the latest in a series of such successes for the Palestinian Authority.
The International Criminal Court has recognized Palestinian membership, and the United Nations recognized the Palestinians as a nonmember observer state. A bid for full recognition failed to get the necessary U.N. Security Council votes