The 35-year-old trained at the club's Hertfordshire base during November to boost his fitness levels following the end of his MLS season with New York Red Bulls.
Henry returned to the Emirates in a loan deal last year, extending his club record goal tally to 228 making four appearances.
Gunners boss Arsene Wenger appeared keen in recent weeks to re-sign the French forward, particularly considering the departure of Ivorian Gervinho this month at the start of 2013 for the African Cup of Nations.
But speaking after Tuesday's lacklustre 1-1 draw at Southampton, Wenger ruled out any deal and said: "He is not ready, he has just come back from holiday anyway. At the moment we are not on that case."
Two months ago, Wenger was full of praise for his ex-pupil, suggesting he was keen to take him on for a third spell at the club.
He said: "You know what Thierry gives you; he gives you hope, especially when he comes on, that is the most important thing.
"Thierry is a communicator, an extrovert, very intelligent. He can only give good advice to players because he was in their position when he arrived here.
"I think now this team has an exceptionally good character. There are not many flashy boys. What is the most important thing is not whether you are an extrovert, but what it means to you to do well, your job, your will to win."