The news is a welcome lift for manager Csaba Laszlo, who has been without the defender's namesake and rearguard colleague Craig Thomson since the end of October.
Defensive injuries have forced Laszlo to turn to youngsters Marius Cinikas and Rocky Visconte in recent matches.
The Jambos boss told his club's official website: "It has been a frustrating time for Jason but hopefully he is nearing the end of this.
"We must be careful with him but it is positive that he is nearly ready again and we will see how he goes this week."
Visconte, meanwhile, has reflected on his first-team debut in Saturday's Active Nation Scottish Cup defeat at Aberdeen.
The 19-year-old Australian, who had only played five behind-closed-doors friendlies this season before the trip to Pittodrie, said: "It was pretty hard against Aberdeen, I struggled with my breathing a bit but it was good. I tried not to do anything fancy and just play straightforward football.
"For a young player like me it's good training full-time with the first team squad, you learn from them.
"There are players like me at all Scottish clubs, just waiting for a chance. Many try to go out on loan but it's not always possible.
"I'm lucky enough to get a chance in the first team but some other youngsters will only play a handful of games a season."
Visconte knows his opportunity has come as a result of injuries to more experienced players.
"I found out on Friday I was starting when we trained at Tynecastle and with Lee Wallace and Andrew Driver injured it gave me an opportunity," he explained.
"It's a big learning curve for me and hopefully I've shown the gaffer I can come in and do a job.
"Sometimes it is frustrating not playing games all the time but if you keep working hard and doing what the gaffer says you'll maybe be lucky enough to get a chance."
Hearts have announced their SPL game with Hamilton had been put back 24 hours to Sunday, February 21 following a request from Lothian and Borders Police, who are dealing with non-sports related events the previous day.
Source: Team Talk
Source: Team Talk