A "desperate" Theresa May has asked the Tories' former coalition partner the Lib Dems for help in getting legislation through parliament, reports The Times.
He is also believed to have spoken to other senior Lib Dems about an informal working relationship, the London Evening Standard reports.
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The Independent reports that "the conversation included the Lib Dem plan to increase income tax by 1p for every earner to raise £6bn for the NHS and social care".
However, although the Conservatives confirmed there have been discussions about working together on areas on which the two parties agree, such as mental health reform, they "vehemently deny that any discussions on tax" took place, says the Times.
A spokesman for the Lib Dems said: "Tim Farron has been very clear - there will be no coalitions, no pacts, no deals."
This "does not preclude conversations about issues on a vote-by-vote basis", he added.
Theresa May's confidence-and-supply partner the DUP is thought to be "relaxed" about the idea of the Tories working across the chamber to push through individual policies.
The Lib Dems have 12 MPs, a stronger parliamentary representation than the Unionists with ten.