The 25-year-old was initially told to aim for pre-season training when he suffered severe knee ligament damage in a collision during Gers' Champions League clash in Stuttgart last November.
But after a stint of intense rehabilitation in his native United States, the former PSV Eindhoven and Manchester City attacker believes a comeback this term cannot be ruled out.
"It's only been three and a half months and the injury's supposed to be six months, so I'm definitely ahead of schedule," Beasley told Rangers TV.
"I'm not going to rush anything - I'm going to take it day by day.
"If I play by the end of the season, great, if I don't it will be a disappointment because I want to contribute to the team.
"If I'm able to play at the end of the season, late April, early May, that's fantastic. I'm definitely shooting for that because I've been out for so long, and I want to play."