The midfielder has missed the last three games with an ankle injury, with the Dons going on an unbeaten run in that time.
The team has taken seven points out of nine and returned to second in the Premiership in Jack's absence, their form returning with a bang following a dire slump around October.
Jack was joined on the sidelines by Barry Robson, who suffered a similar injury at around the same time.
Derek McInnes told RedWeb: "Ryan's done a lot of work over the last couple of days and he's more likely to have a chance to be involved on Saturday than Barry Robson, who hasn't been able to get back on to the training pitch yet so he might be another week."
Meanwhile, Niall McGinn should be available to start against third-placed Hearts – who he terrorised in the away fixture earlier in the season.
McInnes revealed that McGinn was substituted at half-time during the Dons' win over Dundee on Saturday "as a precaution" after the game.