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."
Fabregas revealed he had delayed coming off against Burnley until he had put his team in front.
"I felt something 10 minutes before the goal but I didn't want to leave the pitch until we scored the goal," he said.
"After that I tried to carry on a little bit but it was better that I came off.
"All the time it is the same hamstring and last season I missed the Manchester United game because of the same thing.
"It's four or five times now in the same area. I don't know what's going on but that's why it's better that I take my time and come back when I'm ready.
"It's not that I have strained it, it is just a little bit of fluid that is there and it keeps me out for between five and six days."
The Gunners are right in contention for the Premier League title, just two points behind leaders Chelsea and level with second-placed Manchester United.
Fabregas does not think he or his team-mates should be talking up their chances, but admits the team are driven to succeed for injured colleagues like Aaron Ramsey, Robin van Persie, Kieran Gibbs and Johan Djourou.
"The Aaron thing, Robin, Gibbs, Johan Djourou, they made us more united," he added.
"We haven't seen Robin for four months, we don't know anything about him but Gibbsy and Johan we see them all the time and they would love to be in our position, so that is making us more united as a team.
"Hopefully we can do it for the club, for the fans and also for them.
"We have never talked (about the title), we just kept going and going. But now even more it is the time to be doing our talking on the pitch because we have a great opportunity."