Party bosses will meet on Saturday to hammer out a timetable for the contest, with the expectation that they may delay the start of the race until after the local elections in May.
The contest had been anticipated sooner so the party could begin to rebuild ahead of the local elections.
But senior Lib Dems are understood to be keen to see who is elected as Labour’s next leader in April, before deciding on who is the best candidate to replace Ms Swinson.
A later date would also give the party time to conduct a full review into its miserable electoral showing in December, where Ms Swinson lost her seat to the SNP by less than 150 votes.
“One of the things for candidates will be to decide what is our MO after Brexit,” a party source said.
“It will be ‘big P’ politics. What is the big picture on Europe, climate change? How do we challenge Boris Johnson?”
Sir Ed Davey, who lost out to Ms Swinson in the last contest, is serving as temporary leader until a successor has been appointed, as party rules say the leader must be an MP.
The former cabinet minister is likely to run for the top job, alongside the party’s education spokesperson Layla Moran, who recently announced she was pansexual.
Daisy Cooper, the newly elected MP for St Albans, has refused to rule out joining the race, while Christine Jardine, the Lib Dem Home Office spokesperson, is also thought to be considering a bid.
Candidates must be backed by more than 10 per cent of the parliamentary party, which amounts to only one supporter from the 11 Lib Dem MPs.
The contenders must also be supported by 200 members in aggregate in at least 20 local parties to get through to a membership ballot for the contest.