The La Liga champions have already failed with a £30m bid for the Spain international, who is currently away with his national team at the World Cup in South Africa.
Fabregas, 23, joined Arsenal in 2003 from Barca's youth academy and currently captains Wenger's first team. As such the Frenchman is loath to lose his most influential player, telling ESPN: "What is important is that Cesc has a great World Cup and that he comes back to Arsenal with a great desire to do well for the club.
"We want to keep our best players - that's my huge determination - I built this team for years from 16 and 17 years of age with most of the players.
"We want to continue to work with them because we feel we are very close, and strengthen the team in a very strong way."
While Wenger will do everything in his power to keep Fabregas, he knows the player himself wants to one day return to Barcelona and, should the Spanish club make an offer Arsenal can't refuse, it is more than likely a move will be agreed.