Mikel Arteta had initially suggested that the 24-year-old would be on the sidelines for "weeks", but Hincapie is now pushing to be available for selection when the Gunners host Everton on Saturday after being spotted in training on Friday morning.
"Piero, let's see," the Arsenal manager said. "If he is able to train the next few days he can be available for Everton, which is great news."
Hincapie looked to be in good spirts during the training session and seemingly experienced an initiation with regards to returning ahead of schedule.
The defender was made to run through a tunnel of awaiting team-mates as well as the Arsenal coaching staff as he took in some cheers and a few slaps on the head before the hard work started.
Jurrien Timber, meanwhile, was presented with a special framed shirt to mark his 100th appearance for the Gunners.
Christos Tzolis also remains a doubt having not played for the Gunners since sustaining a hamstring injury while on international duty with Greece.