The abrupt switch after a short stint at the helm for UAE has left the Uniter Arab Emirates Football Association (UAEFA) in the hunt for his successor.
The football governing body will meet next week to decide on a new coach for the Whites.
Van Marwijk has stepped down as Saudi head coach after securing qualification for the 2018 World Cup in Russia and the Green Falcons have moved swiftly to replace him with Bauza.
"There was a request from the Saudi Arabian Football Federation and the UAE FA agreed to co-operate," Hassan Al Jasmi, the UAEFA spokesman, told the Khaleej Times.
"The UAEFA will hold a meeting next week and decide on the future," he added.
The Argentine was named head coach of UAE only in May 2017, and oversaw a 1-1 draw in Thailand, 2-1 victory over Saudi Arabia and 1-0 defeat against Iraq in World Cup qualifying during his short stint.
Bauza and the UAEFA were able to reach a mutual agreement with the Saudis for the Argentinian to take the head coach's seat for the Green Falcons.
The 59-year-old will now prepare the team for the World Cup next summer.
Bauza was contracted with the UAE until the AFC Asian Cup in 2019, which they will host. But attention now turns to who will succeed him.
Reports in UAE claim Shabab Al Ahli Dubai Club coach Cosmin Olaroiu is at the top of the list of candidates.