The Tannadice chief knows his club will take a huge cash hit if a new Rangers were denied an SPL place.
But he's also wary of a backlash from the Tayside club's own fans if the Ibrox outfit were given the nod to transfer its share in the league to a new company.
Thompson said: "This season we got £1.4m from the SPL.
"If we only get £200,000 to £300,000, then how do we fill the £1m?
"Fans are talking about boycotts. It's a lose-lose situation. We are at a crossroads for Scottish football.
"I have a legal responsibility to run Dundee United and a legal responsibility as a director of the SPL.
"We've got to think about our own clubs and about the whole of Scottish football. It is simply impossible."
Thompson spoke out ahead of today's summit of SPL chiefs at Hampden to discuss financial fair play rules and changes to the voting structure.
But there will be no vote on Rangers because no newco has yet to be formed after American tycoon Bill Miller was last week given preferred bidder status by the club's administrators.
Current rules mean that any decision to admit a newco into the top league lies with the SPL board.
And yesterday reports claimed that the board would have no legal power to hit Rangers with further sanctions as a condition of them being admitted to the SPL as a newco.
Thompson refused to say how he would vote on any application to let a Rangers into the SPL.
He added: "I am not willing to show my hand. I am still mulling over everything. We don't know where Sky and ESPN sit. If we did it might make the decision a bit easier."