The German had been told he was free to leave the Emirates Stadium before the close of the transfer window, but injury to Olivier Giroud has prompted a re-think.
Juventus and Wolfsburg were among the clubs interested in signing Podolski.
"Podolski is in the squad tomorrow and will stay with us," said the Frenchman ahead of the second leg of his side's Champions League qualifier with Besiktas.
Giroud will be unavailable until November, with scans by a specialist on Tuesday confirming a broken bone in the France striker's foot.
The equaliser he scored as the Gunners came from behind to draw 2-2 against Everton is expected to be his last first-team action for 10 weeks.
Podolski's immediate position under Wenger has further been strengthened by doubts over Alexis Sanchez's fitness for Wednesday night's clash with the Turkish side at the Emirates Stadium.
Wenger also has Yaya Sanogo and Joel Campbell to turn to in attack in Giroud's absence but neither boast Podolski's experience in Europe's elite competition.