The former France captain, who has played in the United States with New York Red Bulls since July 2010, is Arsenal's record goalscorer with 228 efforts coming from 377 appearances for the London club.
Henry fired Arsene Wenger's side to two Premier League titles and three FA Cups in a prolific eight-year spell, having signed from Juventus in 1999.
He returned to the club on loan in January 2012, scoring twice in a seven-game stint.
A third spell as a player is not thought to be on the cards for the 36-year-old, although Wenger is reportedly keen on bolstering his attacking ranks in January.
Olivier Giroud has netted eight times in 18 games for Arsenal this term, but second-choice striker Nicklas Bendtner is yet to score in seven outings and has expressed his desire to leave the Emirates Stadium when the transfer window re-opens.
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