The shadow home secretary launched the four-letter tirade in a Parliamentary bar after Ms Abbott helped vote through the Article 50 bill.
Mr Davis, MP for Haltemprice and Howden, is said to have moved to kiss Ms Abbott at the Strangers' Bar in Westminster before walking away laughing.
The bizarre incident was reported on Twitter by Paul Waugh, the Huffington Post's political editor.
He wrote: "Vignette from Commons' Strangers Bar: David Davis moves in to give Abbott a kiss. She recoils and tells him to f*** off. He walked away laughing."
When contacted by Express.co.uk, Ms Abbott's office said they were aware of the reports but had no further statement to make.
Diane Abbott reportedly swore at David Davis on Wednesday night in Parliament
We need to be clear, this isn’t Tony Benn Brexit: this is Donald Trump Brexit – and its got a very ugly side
Speaking after Wednesday night's vote, Ms Abbott risked angering Labour voters after she criticised the type of Brexit people had voted for.
“I respect the result of the referendum and no one wanted to thwart it, in a perverse kind of way,” she told Newsnight.
“But we need to be clear, this isn’t Tony Benn Brexit: this is Donald Trump Brexit – and its got a very ugly side.”
The comments from the shadow home secretary illustrates the divide between much of the party leadership and traditional Labour voters who were instrumental in winning the vote to Leave.
Labour leader Jeremy Corbyn imposed a three-line whip on Labour MP’s forcing them to support the government’s Article 50 bill – which passed through the Commons yesterday any amendments.
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Diane Abbott is reported to have issued a withering put down to the government's Brexit secretary
Theresa May has set herself a deadline of March 30 to trigger Article 50, which begins the official process of leaving the trading bloc.
Ms Abbott provoked fury across the House by failing to attend the second vote of the Article 50 bill last week due to ‘illness.
Some speculated that this was due to her opposition to Brexit and the fact her constituency voted overwhelming to Remain. Her office
Her office have stated her absence was simply due to being "taken ill".
Many in her own party said she has jeopardised her role on the front bench, including Labour Brexiteer Kate Hoey, who said earlier this week that Ms Abbott had "embarrassed herself".
Labour was rocked on Wednesday after Clive Lewis was forced to quit the frontbencher after defying the three-line whip.
Diane Abbott's most controversial quotes
Mon, February 6, 2017
Outspoken Shadow Home Secretary, Diane Abbott holds strong opinions which does not always go down well.
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Being an MP is a good job, the sort of job all working-class parents want for their children — clean, indoors and no heavy lifting. What could be nicer?
Mr Lewis, touted by some as a potential future Labour leader, said he could not back the Bill, given his Norwich constituency voted 56.2% to 43.8% to remain in the EU in June's referendum.
He said: "When I became the MP for Norwich South, I promised my constituents I would be 'Norwich's voice in Westminster, not Westminster's voice in Norwich'.
"I therefore cannot, in all good conscience, vote for something I believe will ultimately harm the city I have the honour to represent, love and call home.
"It is therefore with a heavy heart that I have decided to resign from the shadow cabinet.
"It has been a privilege to work with Jeremy Corbyn and be part of the shadow cabinet. I will continue to support our party and our leader from the backbenches to the very best of my ability."