That decision will be taken once a take-over is completed.
That would give Gray another 10 Premiership matches and an FA Cup tie with Arsenal before officials would be forced into reconsidering his position.
United chief executive Trevor Birch has already sounded out Premier League officials about Gray staying on beyond the three-month period.
His chances have been made better by the team's improvement since he took temporary charge and it is hoped a deal can be done quickly to enable whoever takes charge of the team to wheel and deal during the January transfer window.
Gray said: "My position is a day-to-day thing. I am just getting on with the job, which I am finding enjoyable."
Leeds face Fulham and Manchester City ahead of their crucial festive showdowns against relegation rivals Aston Villa and Wolves.
Gray added: "We've got to keep working hard and picking the points up.
"We've had a couple of good results, but the players and I won't be happy until we have enough points to remain in the Premiership next season."