The Spain midfielder missed the 5-0 Champions League victory over Porto in midweek following a recurrence of a hamstring problem and looks set to miss out against Hull in the Premier League on Saturday.
Fabregas is convinced the injury is something that occurs after a concerted run of games rather than because of any particular tweaks or strains, but does not want Wenger to cut back his playing time as the Gunners fight for glory at home and in Europe.
He told Arsenal TV Online: "I never (ask to be rested). I love playing football, I was feeling good (when the injury happened against Burnley) and you never know when that is going to happen. As long as you are feeling good you just want to play.
"It's a little bit better. I'm getting there day by day."