The Light Blues are on the trail of the right-back as Russell Martin looks to the English market in his attempts to make early additions to his squad.
Aarons is a name on the list, out of the picture at the Premier League side having spent time on loan at Valencia last season, not featuring much there either.
Some reports suggested a verbal agreement was even in place for the 25-year-old to move north, but that's understood not to be the case.
But the former England under-21 star is certainly on the radar with a loan move explored by Gers chiefs.
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However, that's where they could hit a roadblock as Sky Sports News are now reporting that Bournemouth would prefer to sanction a permanent exit somewhere for Aarons.
Having moved for £7million from Norwich back in 2023, that could prove difficult to do for Rangers.
Meanwhile, Rangers are also hoping to do a deal for Peterborough winger Kwame Poku.
The 23-year-old is available for a small cross-border training compensation fee and it has been suggested Gers have stolen a march on as many as 30 interested clubs, including Birmingham.