John Macmillan, General Secretary of the Rangers Supporters Association, made the threat today.
And it came in the aftermath of Charles Green's decision to officially snub February's cup tie at Tannadice – but he has hinted the embargo may not stop there.
A run in the Scotish Cup could throw up the prospect of an Old Firm game – the only one possible this season – but even then, the Ibrox support could still vote with their feet if the tie was at Celtic Park.
Macmillan said: "We would hope the boycott would extend to other SPL clubs we might be drawn against, should we progress, and that could well include Celtic.
"But it is early days. The resentment is there about the way we feel Rangers were treated this year and this is our chance to do something abut it.
"We are not singling out one club here. It is not all about Dundee United.
"There were a number of SPL clubs who put the knife into Rangers and hurt them badly.
"The suggestion to boycott will come up again if we are successful in progressing, and that will cover all away SPL grounds.
"All of the SPL clubs made it quite clear this summer that they were voting because they were responding to the wishes of their fans.
"Well, now it is the turn of Rangers to listen to their support and act accordingly."
The latest storm to engulf Scottish football erupted after Rangers decided to reject their allocation of tickets for the cup tie against Dundee United at Tannadice.
Green said: "Everyone at this club is dismayed at the actions of certain SPL clubs, which were actively engaged in trying to harm Rangers when we were in a perilous situation and we are acutely aware of their attitude to us.
"Not all clubs fall into that category and we made Motherwell very welcome when we played them at Ibrox in the League Cup recently.
"However, feelings remain very raw and it should be no surprise that we as a club feel this way.
"The last thing we want is to compromise security arrangements for any match. I therefore appeal to all fans not to travel to this match and to Dundee United not to sell tickets to Rangers supporters."
The boycott announcement last night triggered a quick response from the SFA, who said the matter would be discussed at a meeting tomorrow. But it raises the notion that Rangers could still be entitled to half the gate money at Tannadice – despite their fans staying away.