Rachel Johnson is believed to have held talks with the party about standing as an MP in one of its target seats.
Brexit caused a very public family rift between the Foreign Secretary and his sibling, with journalist Ms Johnson writing that she and her children cried over the referendum result, which her brother campaigned for.
Mr Johnson is credited by many for helping to swing the vote in June for the Leave campaign.
At the time, his sister said her 19-year-old son Oliver had told her: “Boris has stolen our futures.”
Ms Johnson is believed to have called the former Lib Dem leader Nick Clegg earlier this week to discuss the possibility of standing for the party in Bath or Yeovil, Channel 4 reports.
However talks collapsed when Ms Johnson was told she had to be a member for a year before she could stand as a candidate for the party.
The Lib Dems are the only major political party offering voters the chance to reverse the decision to leave the EU. They hope to take seats from both Labour and the Conservatives on 8 June by offering distraught Remain voters a second referendum.
Ms Johnson has previously been a staunch Tory.
She has two siblings in the Conservative Party, as her brother Jo is the current universities minister.
Jo campaigned against Boris last June, calling for Britain to remain in the EU.
Last year, Ms Johnson wrote in her Mail on Sunday column: “In general elections I have voted nothing but Tory, and since I have two brothers standing as MPs for the party, it’s sort of a matter of family duty.”
Ms Johnson has neither confirmed nor denied reports she has joined the rival party. The Lib Dems have declined to confirm Ms Johnson's membership, citing data protection rules.