The Gunners have reportedly agreed a £35m fee for Spanish international Fabregas and a £24m price tag for French international Nasri.
"We hope it will be sorted out very quickly one way or the other," said manager Arsene Wenger of the Fabregas situation.
"The Nasri situation is stable. Again it is very difficult to speak about possible transfers but we are in a situation where we have to make decisions one way or the other. Ideally you want it to be sorted out before the season starts."
The Gunners signed Fabregas from Barcelona's youth system in 2003. The 23-year-old has since gone on to captain the side, making over 200 appearances for the North London club.
Frenchman Nasri moved to the Emirates from Marseille in 2008 for around £12m.