Ms Johnson reportedly hoped to stand as a party candidate in the June 8 election but could not do so because of a rule requiring candidates to have been members for at least a year.
Her move reflects deep differences within the Johnson family over the UK leaving the European Union.
The current Foreign Secretary was perhaps the most prominent campaigner for EU withdrawal in the 2016 referendum, while his father Stanley - a former MEP - sister Rachel and MP brother Jo all backed Remain.
Writing in her column in the Mail on Sunday last June, Ms Johnson said the result made her daughter cry, while her son's friends were blaming Boris for "stealing our futures".
Brexit "feels wrong to my stomach", she wrote.
Liberal Democrats declined to discuss Ms Johnson's move.
She has previously revealed that she joined the Conservatives in 2008, inspired by a dinner party discussion with David Cameron in Notting Hill, but left in 2011 complaining she was treated "like the brainwashed member of a cult".
Reports suggest that Ms Johnson approached former leader Nick Clegg within the past few days and may have been hoping to represent the party in a South West seat like Remain-backing Bath or Paddy Ashdown's former stronghold of Yeovil.
There was no immediate response to a request for comment from the Foreign Secretary.