Aged 40 and two months, he will overtake German Lothar Matthaeus's record, set at Euro 2000.
The balding keeper is universally recognised by his trademark jogging bottoms, first worn to protect his knees from rough surfaces.
Forced one day to change from black ones to grey, he has kept the colour ever since as one of numerous superstitions.
Playing against his country's longstanding rivals will revive happy memories for Kiraly, although his mind will have to delve back a long way.
It was 18 years ago that he made his international debut against the Austrians and saved a penalty from Toni Polster after just four minutes.
Despite a three-year gap between 2006-09, he has slowly added to his tally of international appearances, becoming the most capped Hungarian with 103 and seeing off challengers for the jersey with heroic performances in the two playoff victories over Norway.
Meanwhile, he has appeared for three German clubs and five in England before coming full circle and returning to his first Hungarian team, Haladas.
Having finished only third in their qualifying group behind Northern Ireland and Romania, Hungary are one of the countries to have benefited from UEFA's expansion of the finals to 24 teams, enabling them to reach a first major tournament since the 1986 World Cup.
Austria, in contrast, surprised many observers by strolling through their group.
Nine wins and a draw even propelled them into the top 10 of FIFA's world rankings for June, although they benefited from playing some modest opposition.
Narrow home wins against Malta and Albania and home defeats by Turkey and the Netherlands since qualifying may have dented some of the initial optimism but Swiss coach Marcel Koller is expected to persevere with his high-tempo pressing game.
They will use the versatile Bayern Munich defender David Alaba as a midfielder with licence to go forward in support of Marc Janko, the lanky striker who scored five goals in qualifying.
(Editing by Ian Chadband)
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