Swinson lost her seat in East Dunbartonshire, near Glasgow, in 2015 when she was wiped out by the tsunami of support for the Scottish National Party in the wake of the independence referendum.
But she won it back in last week's General Election, with a majority of 5,339.
Tim Farron stepped down as the Lib Dem leader earlier this week, after accepting the blame for the party's poor performance.
But he also said he felt "torn between living as a faithful Christian and serving as a political leader."
His comments were believed to be a reference to his views about gay sex. During the campaign, Farron was repeatedly asked about his views about gay sex and eventually stated that he did not believe gay sex was a sin.
But the behind-the-scenes row led to Lord Paddick, a former police officer who is openly gay, resigning from the Liberal Democrat front bench, stating that he disagreed with Farron's "views on various issues."
A week ago Farron had ruled out going into coalition with the Tories, who failed to reach the 326 seats required to form a majority in Parliament.
My fav Jo Swinson fact is that partway through her first term, her travel claims shot up — because her Young Persons Railcard had expired.
— The Yorkist 🌳 (@budgettipple) 15 June 2017
The Liberal Democrats increased their number of seats in Parliament from eight to 12 but their overall share of the vote fell and Farron was criticized for failing to have taken advantage of a weak Conservative campaign, especially in the Liberals' tradition heartlands in the South West of England.
The party's former leader, Nick Clegg, even lost his seat in Sheffield Hallam to Labour.
Nick Clegg has LOST his seat to Labour! That's what happens when you sell out the students to the Tories! #LabGain #GE2017
— Jeremy Corbyn for PM (@JeremyCorbyn4PM) June 9, 2017
Clegg had led the party into coalition with David Cameron's Conservatives in 2010 — the first time the party had been in government since 1922, when David Lloyd George was prime minister.
But the party paid a high price in 2015 for going into coalition and agreeing to numerous unpopular policies associated with austerity, including a U-turn on university tuition fees.
I for one will be whole-heartedly supporting @joswinson should she choose to run. Experienced, excellent communicator, brilliant liberal.
— Harry Samuels (@CuriousCabbage) 14 June 2017
They lost 49 of their 57 seats in Parliament and have been struggling to rebuild.
Some in the Liberal Democrats have suggested a "dream team" of Swinson and Sir Vince Cable, who at 74, might be considered to be too old to lead the party himself.
Cable also regained his seat — at Twickenham — in last week's election.
"Good luck Vince!"
— Vince Cable (@vincecable) June 8, 2017
The energy throughout the campaign has been tremendous — from the knocking on doors to the support here on social media. pic.twitter.com/NqgfUSbZ3r
But the focus remains on Swinson, who has a three-year-old son. She nearly died in 2013 when she suffered a violent reaction as a result of a peanut allergy.
Liberal Democrat GAIN East Dunbartonshire from SNP.
— Britain Elects (@britainelects) 9 June 2017
Jo Swinson back in. pic.twitter.com/ThdiuIC2Wa
She is expected to face a challenge from Sir Ed Davey, a former Energy Secretary, and former health minister Norman Lamb.
Several grandees within the party apparently believe she would represent an invigoratingly fresh, and female, face of a party, which saw many of his younger voters drifting away to Labour under Jeremy Corbyn.
But some critics have already pointed out her conservative (with a small c) voting record — she voted against increased income tax for those earning over US$190,000 (£150,000) voted against a tax on banker's bonuses, and voted against restricting the fees landlords can charge tenants.
