Henry, who was on hand to watch Arsenal demolish rivals Tottenham 5-2 last weekend, rejoined his old club last January on a two-month loan spell from the MLS side and scored twice in seven appearances.
The 35-year-old is again looking to maintain his fitness during the MLS off-season and has been training with Arsenal, but new Red Bulls sporting director Andy Roxburgh is reportedly apprehensive about him returning to the Emirates and favours him resting over Christmas and New Year.
With forwards Gervinho and Marouane Chamakh expected to go to the 2013 African Cup of Nations and Arsenal reaching the last 16 of the Champions League, Wenger said he was contemplating adding an additional striker to his squad.
"I just spoke about that (a second Henry loan spell) because people asked me," Wenger told the club's website on Thursday.
"I said I don't rule it out because he's in good shape but I haven't made up my mind yet.
"I haven't spoken to Thierry about it. I just answered a question honestly that I have not completely decided how I will sort it out in my head.
"We are maybe looking at a striker because Gervinho is going to the Africa Cup of Nations."
Used by Wenger as an impact player from the bench last season, Henry netted late winners against Leeds in the FA Cup and Sunderland in the Premier League.