In an article published in The Times newspaper today, it was suggested a commission will consider four options for the future of the party in Scotland in the wake of leader Ruth Davidson's departure.
These include two separate parties with a coalition agreement at Westminster and an arrangement where one party stands for the Scottish Parliament and the other for the Commons, according to the paper.
Writing in The Scotsman at the time, Mr Fraser said a "Canadian model" could be used, comparing it to Quebec Conservatives voting for the Quebec Liberal Party.
Mr Brown said the move would represent a "double standard" for the Scottish Tories.
"This is gross hypocrisy from the Tories, who are now demanding independence from their Westminster bosses at the same time as trying to block the people of Scotland being given a say on their future," he said.
"Boris Johnson's Government is too toxic for Ruth Davidson - and now it seems it is too extreme for the Scottish Tories as a whole.
"But however they try to dress this up, the Scottish Tories cannot escape the enormous double standard in wanting independence from Westminster while simultaneously trying to deny Scotland that democratic choice."
"And even if they do split from their UK bosses, no-one would be fooled. They would still be taking their orders from Westminster and lining up beside Boris Johnson in any election."
Speaking on STV's Scotland Tonight programme on Thursday, Scottish Conservative MSP Annie Wells rejected the idea of a split.
Ms Wells said: "I think we work well together. I think we can work well together.
"I think there are certain different characters in both the Conservative Party in Westminster and the Conservative Party up here but I don't think there's a need to actually split the family of conservatism, no."