The centre-back according to SunSport will pen a two-year contract with the Gers.
The 32-year-old is a free agent after his contract with Brighton & Hove Albion expired at the end of the season.
Rangers have been looking for a new defender with Nikola Katic injured and facing months on the sidelines.
Balogun joined Wigan on loan in January after failing to secure regular playing berth at Brighton.
German-born Balogun is hugely experienced having been capped 32 times for Nigeria, who he qualifies to play for through his father.
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