The Gunners' 2-0 win at Anfield on Sunday condemned the Reds to their worst start to a season since 1962-63.
Rodgers' team head into the international break in the relegation zone and, after a disastrous final two days of the transfer window when they allowed Andy Carroll to join West Ham before failing to secure the anticipated replacement, major questions are suddenly being asked of the Merseysiders' new boss.
"I faced this last year in the same period," said Wenger, who 12 months ago was licking his wounds after an 8-2 hammering by Manchester United.
"He (Rodgers) has just arrived at this club. Of course the expectations are very high but you just want to tell people to keep confident and stand behind the man.
"When he comes to a big club it is important that he feels that people trust him. I am sure he will turn it round."