The midfielder, who it is understood does not currently employ an agent and looks after his own affairs, has been linked with interest from Aberdeen since the turn of the year and has not yet committed himself to a new agreement at Tynecastle.
Jefferies has told all the players whose deals are close to finishing – including Laryea Kingston, Christian Nade and Marian Kello – that their performances over the remaining five fixtures could determine their future.
However, the manager has also acknowledged that Stewart, currently sidelined with a calf injury, and the other players will themselves have a big say. He said: "Michael is out of contract. He might want to move on, he might have offers. Once he gets back fit and playing we'll take it from there. It's not just about the club wanting to keep players. They might have offers coming in and other things to consider."
Meanwhile, Hearts fans face a scramble to secure tickets for the final Edinburgh derby of the season against Hibs after being given less than a quarter of their usual allocation for the crucial match.
The Tynecastle outfit have been granted just 773 briefs for the 1 May encounter, which could go a long way to deciding which of the three clubs chasing Dundee United go on to qualify for next season's Europa League.
Hearts normally receive almost 4,000 seats but, because of Hibs' work to redevelop their east stand and the housing of home fans in the south stand, Jefferies' team will have to make do with a vastly reduced following.