Mooy wasn't involved in Australia's goalless draw against Colombia at Craven Cottage last night after suffering a "minor injury setback".
The winger is now being assessed by Huddersfield ahead of Saturday's game against Newcastle United.
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Mooy had a spell out last month with an infection in a knee he cut against Bournemouth.
The 27-year-old is a key player for Huddersfield manager Wagner, whose side is 15th in the Premier League table and a point behind 13th-placed Newcastle.
Mooy's midfield colleague Philip Billing returned home early from international duty with Denmark's Under-21s after suffering an injury.
Meanwhile, United are "assessing" winger Matt Ritchie after the winger withdrew from the Scotland squad with an unspecified injury.