Writing on Twitter, the Scottish Tory leader dismissed the newspaper claim as "b****cks".
She said it had been decided when she became leader that "we (the Scottish party) would have complete autonomy over policy, candidates, campaigning, finance, which is what we have ... but we would take the Conservative whip at Westminster and that is exactly what is going to happen".
The First Minister was forced to admit a massive backlash against her referendum demand was "undoubtedly" a factor in her party losing 21 MPs, including Mr Salmond and Angus Robertson, and pledged to "consider very carefully" her next steps over the coming days.
Conservatives are forecast to lose 12 seats, a turnaround from earlier predictions it might gain as many as 100.
"If you take away the 13 seats that were won by Ruth Davidson, right now we couldn't even be forming a coalition with anyone", said the party source.
In an early indication that she might seek a greater influence in the United Kingdom party, Ms Davidson said on Friday she had been given assurances that any Conservative deal with the Democratic Unionist Party (DUP) would not affect LGBTI rights. "Theresa May and her team are fully aware of that fact".
Tehran Attackers are Iranians who Fought Alongside ISIS
The Islamic republic's elite Revolutionary Guard has accused regional rival Saudi Arabia of involvement in Wednesday's attacks. Meanwhile, Iran's interior ministry said Friday that a total of 41 suspects linked to the attacks have been arrested.
May called the snap general election in an attempt to strengthen her hand in forthcoming Brexit talks - and quell the nationalists' ongoing agitation for a second independence referendum. "And that means we can look again at what it is we hope to achieve as we leave the European Union - and I want to be involved in those discussions".
Davidson led her party to its best result in Scotland for three decades, in contrast to Conservative Prime Minister Theresa May's dismal showing elsewhere in the UK.
The source believes Davidson will be willing to dangle the threat of withholding the support of her MPs in parliament if her preference for a softer Brexit, which lessens any impact on Scotland's economy, isn't listened to and acted upon on.
"We will work with others if it is at all possible to keep the Tories out of government", Sturgeon said.
"Ruth's stance on Brexit is clearly different - she signalled to May and the Brexit ministers that she needs to be in play", said the source.
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