He added there would be "difficulties" in arranging a co-hosting of the World Cup by a consortium of countries to include North Korea, but admitted the message of peace "can be a very powerful message".
Infantino was quoted as saying he will sound out Chinese President Xi Jinping about Moon's idea when the two meet later this week.
Its deployment began this April, but South Korean President Moon Jae-in's government called for its suspension on June 7 in order to study its environmental impact, although a part of the system that was already deployed remains operational.
Moon said Japan should look squarely at the comfort women issue and that both countries should understand more time is needed on this issue.
Japan and South Korea struck the landmark deal in December 2015 to "finally and irreversibly" resolve the long-standing comfort women row.
Moon pledged during his election campaign to renegotiate the agreement, which was reached under his predecessor, Park Geun-hye, and has been criticized for not reflecting the voices of the affected women.
Earlier this month, the UN Security Council expanded targeted sanctions against North Korea after its repeated missile tests, adopting the first such resolution agreed by the United States and China since US President Donald Trump took office.
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With the DUP providing the Conservatives a narrow, but crucial, majority in Parliament, it could have an outsized influence. Gove, who was dismissed when May became prime minister past year , will now serve as environment secretary.
North Korea is believed to be operating more than 300 drones for military purposes, either for surveillance or the delivery of attack weapons. "But this is just not a long distance for its strike today", the statement said, hinting that North Korea has ICBM capability.
The issue of the women has plagued bilateral ties between the neighbours for decades.
Nikai arrived in South Korea on Saturday for a four-day visit.
The declaration, it said, is "the foundation of national reconciliation and unity" and "starting point of solving the issue of the north-south relations". Moon was meeting Toshihiro Nikai, the secretary-general of Japan's ruling Liberal Democratic Party, at Cheong Wa Dae on Monday.
He spoke about the need to "exterminate a handful of people plotting schemes" to block Japan-South Korean ties from moving forward.
The two leaders will also discuss ways to advance economic cooperation between their two countries.
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