Tom Hughes says building a new stand cost Partick £1m
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Partick Thistle have offered to accept relegation - as long as the Scottish Premier League pays £1m compensation.
The 12 SPL clubs will vote again on whether to accept Inverness Caledonian Thistle's promotion bid.
But Partick chairman Tom Hughes said: "We are currently members of the SPL and the law is in our favour.
"But, to resolve the impasse, I would be willing to recommend to our board that we support a resolution giving us £1m compensation."
Partick had vowed to take their battle to court if Inverness win their appeal to the Scottish Football Association - or they lose the new vote on 22 June.
SPL rules requiring a 10,000-seat stadium had forced the First Division champions to come to a groundsharing agreement with Aberdeen.
That agreement was reached after the 31 March deadline for clubs desiring promotion to meet stadia criteria and that weighed heavily with some clubs as five originally failed to support the Caley Thistle application.
Partick say the £1m would be compensation for the amount spent by the Glasgow club when they were forced to a build a new stand to win promotion in 2002.
Hibernian and Hearts asked the SPL for a second vote, following confusing about how the votes were cast and after the decision faced much public criticism, including a petition containing more than 11,500 supporters.