Hearts manager Gary Locke believes Jamie Hamill will accept a pay cut to stay at the financially-troubled club.
The right-back is due to follow Jamie MacDonald and Ryan Stevenson in agreeing a reduction in salary in order to help the club, who went into administration this week, survive a cashflow crisis.
There was a glimmer of hope for Hearts, though, as it emerged former Scottish Rugby Union chief executive Gordon McKie was leading one of the groups interested in taking over the club.
Locke said: "We are nearly there but are meeting tomorrow to finalise things.
"It's not the sort of thing a snap decision can be made on but the signs are encouraging.
"Fair play to Jamie Mac' and Ryan - these are the types of guys you want in your team and hopefully we'll have more positive developments tomorrow."
Administrators BDO were planning to make four players redundant - two senior players and two youth players - as well as asking the highest-paid players to take cuts, but joint-administrator Bryan Jackson has revealed there could be a total of five going.
Marius Zaliukas and Andrew Driver, whose departures were already inevitable, are expected to have their contracts terminated slightly early while the future of striker John Sutton - another of the top-earners - remains unclear.