The former West Brom youngster signed for the Dark Blues on a short-term deal last summer, and his deal is up at the start of next month.
His potential availability has caught the attention of several clubs, including Colchester, Oxford United and Gillingham.
Easter Road No.2 Garry Parker suggested last week that the Capital club would be looking to strengthen in January.
Hibs are in pole position for Nabi’s signature, according to reports, as Neil Lennon looks to bolster his squad after a seven-game winless run that ended with a 1-0 win away to Hamilton.
However, the Gills are keen to take the Birmingham-born player back to England following spells at Peterborough and Nuneaton Town.
Nabi has netted once for Dundee in ten matches.