Murdo Fraser has admitted he did not have "much real expectation of winning" the Scottish Tory leadership contest.
The leadership hopeful is just two days away from finding out whether he will be chosen by party members to replace Douglas Ross.
However, writing for The Scotsman on Tuesday, the veteran MSP said he went into the contest knowing his chances were not good.
The contest, which also includes former deputy leader Meghan Gallacher and the party's justice spokesman Russell Findlay, comes to an end on September 27.
Mr Fraser wrote in the Scotsman: "I entered the contest late without much real expectation of winning, it being clear from the outset that the party establishment had already decided that Russell should be the man to succeed Douglas Ross."
However, he said the backing of many MSP colleagues and party members compelled him to run.
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During the five-week battle, the contest has been marred by what the candidates described as "blue on blue attacks" with Mr Fraser stating the "party establishment" had already decided rival Mr Findlay would win.
Mr Fraser also came under fire early into the leadership race when he urged his two rivals to drop out of the contest to endorse him in a "coronation" while avoiding a potentially damaging campaign.
Former candidates Liam Kerr and Jamie Greene announced during Mr Fraser's campaign launch that they would not run to instead endorse the Mid Scotland and Fife MSP.
But Ms Gallacher and Mr Findlay refused to step aside, leading to a contest, with hustings all across the country.
While Mr Fraser's column did not state he had formally conceded he would not win, he took aim at the "establishment" of the Scottish Conservatives.
He also put stark warnings in place for his party, arguing low membership numbers of under 7,000 should be a "wake up call" of the challenges ahead.
The total membership numbers have not been confirmed, however MSPs have said it is less than 7,000.
Interim figures from last week suggested just one in three - around 2,400 - had already cast their ballot.
Mr Fraser wrote: "The fact that party membership in Scotland has dropped below 7,000 should be a wake up call to whoever takes over as leader.
"We cannot expect to attract new members if they don't feel that their views count, which is why internal is essential."
Mr Fraser also urged the future leader not to adopt an "anti-devolution" sentiment amid the treat of Nigel Farage's reform party.
He wrote: "If Nigel Farage's Reform UK party campaigns on an 'abolish Holyrood' ticket, that would pose a real challenge for the Scottish Conservatives.
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"But it would be potentially disastrous for my party to lean in to anti-devolution sentiment."
Polling suggests the Tories could achieve around just 12% in the 2026 Scottish Parliament elections, which could see around half of the current 31 MSPs lost.
Meanwhile, several polls suggested Reform could win around 11 seats.
Mr Fraser said a "small but significant" section of Scots were sceptical about devolution, and may have typically backed the Tories at Holyrood.
"But if Reform run on an 'abolish Holyrood' ticket, they may find there are enough sympathetic voters to grant them a clutch of seats in the very institution that they despite," he wrote.
"This is a real challenge for the new Scottish Conservative leader."
He added: "Tempting as it may be to some, it would be counter-productive and potentially disastrous for us to chase Reform votes by leaning in to anti-devolution sentiment, alienating us from mainstream Scottish opinion.
"Our approach instead should be to talk about the better use of Holyrood powers."
He also said the new leader will have many errors to put right, after the contest "shone a light into some dark places which needed the antiseptic of exposure", including the treatment of women.
It follows Ms Gallacher lodging a formal complaint against the conduct of shadow Scottish secretary John Lamont.
Ms Gallacher warned senior party members were briefing against her to state she would drop out to endorse Mr Fraser.
It understood the MSP reportedly accused Mr Lamont of this, and said during a subsequent phone call to discuss the matter, she felt Mr Lamont threatened the future of her political career.
Mr Lamont has strongly denied the allegations and has threatened legal action.
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