Lehmann, 41, has been a free agent since retiring in 2010 after two years with German club Stuttgart.
Manuel Almunia is currently Arsenal's only fit senior goalkeeper because of injuries to Wojciech Szczesny, Lukasz Fabianski and Vito Mannone.
"Lehmann is training with us and will sign for the rest of the season," said Wenger. "We have no cover in the Premier League, so that is why I decided to bring Jens back. He has not signed, but a contract has been agreed."
Lehmann made 199 appearances for Arsenal between 2003 and 2008.
The former Germany international won the Premier League title in 2004, as well as the FA Cup in 2005, but left the club in 2008 after losing his place to Almunia.
Should he sign in time, Lehmann could be named in Arsenal's squad for the Premier League trip to West Bromwich Albion on Saturday.
Arsenal trail leaders Manchester United by three points in the Premier League title race, but have a game in hand.
The Gunners were recently eliminated from the Champions League and the FA Cup, having also lost 2-1 to Birmingham City in the League Cup final.
There was further bad news for Arsenal as Wenger revealed that Belgian centre-back Thomas Vermaelen will not play again this season due to an Achilles tendon problem that has kept him out since September.
"For Thomas Vermaelen the season is over," said Wenger at a press conference.
"In fairness he has not played since September. I never expected him to be fit before the end of the season.
"He is not out on the field yet and it is impossible after six months without competition. I am confident he will have a full recovery but for this season we cannot rely on him."