All those who failed vetting will have appeals heard by senior party members next weekend.
Mr Davidson, MP for Glasgow South West, will appear in support at the appeals of two local councillors, Tommy Morrison and Stephen Dornan.
He told the Herald: “I’m appalled at what has happened with the vetting of sitting councillors. “Labour faces a very difficult election in Glasgow in May given that the SNP was well ahead in the Scottish Government elections, and I don’t believe that the answer should have been to form a circular firing squad.
“I don’t believe that Labour can purge its way into power, and I think there’s obviously other agendas operating when good, hard-working and conscientious local councillors are being dumped from the panel [of would-be candidates].
“There should not be top-down, centrally imposed control in this way, with favourites being allowed through and others being rejected.”
Mr Davidson is considering whether to stand for the deputy leadership of the party in Scotland.
At the moment, the frontrunner is Anas Sarwar, although MSPs Lewis Macdonald and Elaine Murray have also put their hats in the ring.
“I’m told that the deputy leadership is all carved up, but I see that as more of a challenge than anything else,” he said.
“It is simply bad practice to have an important election like this carved up before any ordinary members or trade union members have an opportunity to express an opinion.”
Cllr Graeme Hendry, the SNP whip on the council, said Mr Davidson’s comments showed “a clear breakdown of trust” within Glasgow Labour.
“The chaos reflects the lack of local leadership. “Labour say their recent review will bring the party together, well good luck with that.”
Anas Sarwar said: “The selection process needs to take its course. Whatever happens we need to have a strong group of candidates.”
Asked if the deputy Labour leadership had been “carved up”, he added: “Absolutely not.”
A Scottish Labour spokesman said: “Being a labour councillor is not a job for life, and party members in Glasgow - who select the candidates to field - want change. Those people who do not get selected have the right of appeal but no-one should underestimate our determination to field the best possible set of candidates.”