The Evening Times are reporting the Ibrox club are keen to get Wright this month rather than wait until his contract expires in the summer. The 23-year-old is in the final six months of his contract and Aberdeen manager Derek McInnes has all but given up hope of getting the playmaker to sign a new deal.
Rangers can offer a pre-contract and have already stated their intentions to Aberdeen, but would rather bolster their squad immediately.
Along with a potential return of Stewart, who has twice played under McInnes at Pittodrie, it has also been reported that outstanding money due from Aberdeen for the signing of Ross McCrorie could be waived by Rangers as part of the deal.
Stewart played regularly under Steven Gerrard last term but has only managed to feature four times this campaign.