Traore was rumoured to on the verge of leaving Arsene Wenger's side on loan in August but is pleased no deal materialised.
"I have spoken with the boss and he has told me that the position of official second-choice left-back is there for me," he told the club's official website.
"That doesn't mean it will be always though, so I must just keep trying hard in training and when I am asked to play there, just show that I can do it.
"I think I am going to stay at Arsenal and still try to keep improving every day in training.
"I wanted to do that rather than go on loan, but when I speak to the manager and if he tells me that it has to be done, then of course it will be done."