The 34-year-old Henry, who played for Arsenal from 1999 until 2007 and is their all-time record goal-scorer, would be eligible to play for the Premier League club during Major League Soccer's close-season from Sunday when the January transfer window opens.
"It's a two-month loan deal - the paperwork needs to be done, the agreements, the insurances, I don't take care of that, but that is not completed," Wenger told a news conference.
"We have to respect all of the agreements with the MLS and Red Bulls to finalise it, so we cannot announce it yet, it is not done.
"We are doing it because Marouane Chamakh and Gervinho are going to the African Nations Cup and he will be ideal cover for two months.
"He has experience, quality, he knows the club, he can help the players on and off the pitch, and that's basically it."
Henry played 369 times for Arsenal during his eight years in North London, scoring a club record 226 goals and winning two Premier League titles and three FA Cups. He then spent three seasons at Barcelona before joining New York Red Bulls last year.
Although the former France international could play at Fulham next Monday, Wenger hinted a more likely return could be against Leeds United in the FA Cup Third Round on January 9 or the Premier League match at Swansea on January 15.
Asked how close he was to match fitness, Wenger replied: "He needs two good weeks work."
Wenger continued: "It can only be positive because he has exceptional talent and is a very intelligent man and he has the desire to help the club, but it is difficult to measure how positive his influence will be.
"We will not put too much pressure on him. He is here to help out, he will not be the main player in the squad.
"I respect his desire to help us to get through the period where we lose two strikers, but he is 34 years old. He has not lost his class or his brain and that will be just enough for us."
"He still has good pace. He had exceptional pace but what you lose with age is the capacity to repeat it."
Henry has been training with Arsenal for the last three weeks and was moved to tears this month at the unveiling of a statue in his honour at Emirates Stadium.
"I was fortunate to win a lot of stuff in my career, but this tops it all," he said when the statue depicting him kneeling after scoring a goal was unveiled.
"You can't even dream about it. The statue of me kneeling in front of the stadium is a great honour because that is exactly how I feel about Arsenal Football Club."
Arsenal have recovered well after a poor start to the season and are currently fifth in the Premier League after just one defeat in their last 11 matches.
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