Ms Davidson, who has been in place as leader of the Scottish Conservatives since 2011, is set to step down as head of the party due to the pressures of being a new mother and the struggle to bridge significant differences with Prime Minister Boris Johnson, the Sun reported.
The BBC claims the Edinburgh Central MSP, who steered the party to its best ever Holyrood result in 2016 and their best Westminster result for almost 40 years in 2017, when they returned 13 MPs to the House of Commons.
Chris Green, reporter for the i, The Scotsman's sister paper, confirmed with Tory sources that Ms Davidson would resign and give a statement tomorrow.
He added: "I understand she was already planning to quit before today's row over suspending Parliament."
Ms Davidson, who gave birth to her first child, son Finn, with partner Jen Wilson last October, has previously spoken of how her priorities had changed as a new mother.
This was cited as a partial reason for her looming departure, but her well-worn disagreements with Boris Johnson are understood to be a significant factor.
The pair first clashed during a debate in advance of the Brexit referendum in 2016, where Ms Davidson famously accused the now-Prime Minister of lying.
Ms Davidson has also made clear her opposition to a no-deal Brexit, and her resolve to leave is understood to have been hardened by today's developments, when Mr Johnson suspended Parliament in a move that opponents say is designed to force through a no-deal Brexit.
Many commentators had previously touted the former journalist as a future Prime Minister, citing her strong performances in the 2016 and 2017 elections and her perceived appeal in areas not considered Conservative strongholds.
She is expected to confirm she will remain the MSP for Edinburgh Central until the end of the current Holyrood session.