Hibernian can request to play their final Championship fixture on the same day as Rangers, says Scottish Professional Football League chief executive Neil Doncaster.
Hearts v Rangers is now on 3 May but Falkirk v Hibs remains on 2 May.
Hibs and Hearts feel that jeopardises "sporting integrity" as Rangers could know the result they need to get.
"If clubs want games moved to Sunday they only need to tell us," Doncaster told BBC Scotland.
"We've so far put two requests into Hibernian to ask whether they want their game moved to the Sunday, and as of this morning (Thursday) I've had no response to that.
"We emailed all the clubs in the Championship and asked them if they would like to see other games moved.
"The only comment we've had back to date has been from one of the other clubs involved who have said 'no, we would prefer our game to remain on the Saturday'."
Falkirk chairman Doug Henderson says his club is "strongly opposed" to their match at home to Hibs being moved to Sunday 3 May.
|SFA chief executive Stewart Regan|
|"My preference is that, in a play-off situation, having games finishing at the same time would be the preferred solution."|
Scottish Football Association chief executive Stewart Regan believes the final day fixtures should be played on the same day.
"My preference is that, in a play-off situation, having games finishing at the same time would be the preferred solution," said Regan.
"Sporting integrity is fundamental to any competition and I think that has to be considered in the round.
"The clubs have made their feelings known; I'm sure Neil and his colleagues will listen to what their member clubs have said and come back with a pragmatic proposal."
Doncaster denied that the SPFL is in "a shambles" over the situation.
"No I don't accept that at all," he said. "We've had a request from the broadcasters to move one game to Sunday for television. I don't think that should surprise anyone.
"Hearts against Rangers is one of the biggest Championship games this season; it's the game that Hearts will receive their divisional trophy and it's a big game anyway.
"So I think we should be entirely unsurprised that the broadcasters have selected that game for television.
"The SPFL could have moved all five Championship games from the Saturday to the Sunday, but that would have been absolutely unfair to a number of clubs.
"The reality is that Alloa v Cowdenbeath and Dumbarton v Raith Rovers - there's no possible way that Hearts v Rangers can have any bearing on them."