The Gunners goalscoring legend is currently in the MLS off-season with the New York Red Bulls, but could return to Arsenal to train.
Last season, Henry joined Arsene Wenger's side on loan in January, and the club's all-time leading scorer bagged two goals as he deputised for Marouane Chamakh and Gervinho - both of whom were at the Africa Cup of Nations.
And the report suggests Henry has been informed by Arsenal that he is more than welcome to continue training at London Colney during the off-season, as he looks to maintain his fitness.
There may even be an opportunity for Henry to extend his stay into a second loan spell with the Gunners, as Arsene Wenger is thought to be keen to add a centre-forward to his squad in January.
The north London club have been linked with Atletico Madrid striker Adrian, but they could offer Henry a route back to the Emirates Stadium if they fail to secure their top target.
Henry has just finished his third season in New York. And this year was his best yet, ending in a MVP award nomination for the Frenchman.
The 35-year-old is yet to enter talks with Arsenal, but the report claims he remains an option for the Gunners when they lose Gervinho again in the New Year to the Africa Cup of Nations.
Henry returned to London last week, following the Red Bulls' play-off defeat, and the former France international was in the stands at the Emirates Stadium as Arsenal beat north London rivals Tottenham 5-2 in the Premier League.
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