FIFA's annual Congress voted to back – by a majority of 73 to 27 percent – a proposal that pushed football's governing body to report by March 2018, but Infantino said feedback would come before then.
"We will take responsibility and we will take a decision on this matter," he said, adding FIFA would rule in October.
The Palestine Football Association (PFA) argues that the presence of six Israeli clubs on its territory is in breach of FIFA statutes, which forbids another member association playing on another territory without permission.
Israel argues that FIFA rules are unenforceable as there is no permanent border.
The Congress heard from both the Palestinian and Israeli federations before taking the vote.
Palestinian football chief Jibril Rajoub told delegates his association wanted the same rights as others.
"We are not looking for suspension or expulsion but the full recognition of our right that no Israeli clubs play in our territory," he said.
"None of you will accept that any clubs play in your territory."
However, Ofer Eini of the Israeli association, said the PFA was looking for a political solution.
"The sole purpose is to establish the political boundaries," he told the Congress.
"This is outside the authority of FIFA to establish borders.
"What are you trying to stop five or six teams of children from playing football? Will that resolve the Palestinian problem?"
A FIFA commission chaired by South Africa's Tokyo Sexwale has presented several potential solutions and a fresh report was handed to the FIFA Council on Wednesday, said Infantino, without giving further details.