Galloway has flourished since joining the Mariners from Melbourne Victory early last season, starting in all but one game and attracting attention abroad.
The former youth taekwondo champion had been due to join Josep Gombau's Olyroos training camp this week but was given permission by both Football Federation Australia and the Mariners to travel to the Netherlands.
If successful with his trial, Galloway could be the sixth Australian to play in the Netherlands' top flight next season, joining championship-winner Brad Jones, Sparta Rotterdam duo Craig Goodwin and Kenneth Dougall, Groningen's Ajdin Hrustic and NEC's Stefan Mauk, should they survive the relegation play-offs.
Meanwhile, Hrustic's Groningen team-mate, and Australia's FIFA World Cup defender, Jason Davidson is heading back to Huddersfield Town.
Galloway signed with the Mariners ahead of round three of the 2016-17 A-League season and made 24 appearances for the club, scoring twice in the process.
Mariners coach Paul Okon has also been in Europe on a scouting mission to try to shape his own squad ahead of his second A-League season.