Ljungberg, who won the title twice under Wenger, told ESPN: "If he gets a great opportunity somewhere where they spend more money and win things, maybe that's a possibility. At the same time he likes to bring up new players and he has been at Arsenal a long time.
"I know he is a winner; he always wants to win - just as much as the players. He gets as angry as the players when we lose.
"When they are not winning, or they are fourth or fifth, I know he is not happy about not winning."
Ljungberg, now at Major League Soccer side Seattle Sounders, continued: "Maybe it's harder. If you look at the money they are spending, they are not spending as much as before.
"Maybe it puts more pressure on him (Wenger); maybe he can't get exactly what he wants all the time; maybe he could a bit more in the past."
"In my opinion he is a great, great manager. Of course I'm upset at the moment that they are not doing that great, and it's a sad thing.
"For my career, he helped me so much. When I was young he showed me certain things that you learn when you are older in the game. For me, he is one of the best managers in the world."