Wenger managed to prevent Fabregas from returning to his boyhood club Barcelona last summer, but will have a real fight on his hands if he is to convince the Spaniard to stay at Emirates Stadium for another season as their Premier League title bid slips away.
Fabregas, who took over the Gunners armband in November 2008 aged only 21, recently suggested Wenger's failure to bring in established players is the reason for their lack of trophies.
While Wenger continues to stand by his philosophy, he admits his skipper, who turns 24 on Wednesday, is still too young for such responsibility and has been weighed down by the burden of captaining the young team.
"Maybe this season has been a bit of a heavy burden for Cesc, he puts too much pressure on himself," Wenger said.
"It's too much pressure for someone his age. But he is captain and [Robin] van Persie is vice-captain so they put a lot of pressure on themselves. It's all self-inflicted. Cesc is a winner. He wants to win, he is desperate to win. And of course when it does not work, he is frustrated."
In a bid to tempt his star midfielder to stay, Wenger has promised to bring in more experience in the summer after the club look set to finish a sixth season without silverware, having seen all four trophies slip from their grasp in the space of less than two months.
"We'll try to certainly bring in some more experience," Wenger said. "One of the reasons I took [Jens] Lehmann back was because he has done it.
"Some managers think if a player wants to go he has to go but I believe that this team has been educated and grown together. They are very young. The biggest achievement for them will be to win together. I think they will have learnt their job the hard way.
"Once they win, they will be stronger. The pressure is too much on Cesc at the moment because it doesn't go as well as we want. But once it will go well, he will grow with it. Every difficulty in life will make you stronger, especially when you have a strong character."