The 34-year-old New York Red Bulls striker has been training with the Gunners in order to maintain his fitness during the MLS off-season.
Boss Arsene Wenger is facing a striker shortage in January with forwards Gervinho and Marouane Chamakh departing for the African Nations Cup.
That will put further pressure on top-scorer Robin van Persie, whom Wenger is determined to try and nurse through the rest of the season.
With Henry not due to return to the MLS until March, Wenger sees his fellow countryman - the club's all-time top goalscorer - as an ideal short-term solution.
Reports today suggest negotiations are ongoing between the Gunners and the MLS and a deal could be completed within the next two days, with a potential debut pencilled in for the clash with Leeds United in the FA Cup Third Round on January 9.
Henry first joined the club in 1999 from Juventus and hit 226 goals in 370 appearances before moving to Barcelona in 2007.