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He was previously called up to the Irish squad to face Bulgaria in August.
19-year-old Mulligan has made just appearance for Dave Jones' Wolves - coming on as a substitute in the Championship draw with Burnley back in August.
Rushden, who lie fourteenth in the table, could do with someone of Mulligan's ability and manager Ernie Tippett hopes the Irishman can do well.
"Gary trained with us today (Thursday)," he told the club's website. "He's an up-and-coming prospect at Molineaux and we expect him to do well. We'll reassess the situation after the month's period ends."
Mulligan is expected to line out in the Diamonds' Saturday meeting with struggling Chester City.
The Dubliner famously struck three goals in three games for Sean McCaffrey's Ireland Under 19s last May in Belgium, but their European championship dream died a death as the hosts defeated them 1-0 to send them out of the second phase.
(*Photo courtesy of wolves.co.uk)