Tim Farron said he was "ruling nothing in and ruling nothing out" but was "determined to play a big role".
Mr Farron held his Westmorland and Lonsdale seat with an 8,949 majority.
Mr Clegg resigned in the aftermath of his party's crushing general election result, where it was left with just eight MPs from the 57 it had in 2010.
Other possible replacements are Orkney and Shetland MP Alistair Carmichael, who was Scotland secretary under the last government, and Norfolk North MP Norman Lamb, who was care minister.
Speaking on Sky News, Mr Farron said the Lib Dems had gained 2,500 new members since polling day.
Who will replace Nick Clegg as leader?
"History will be kinder to the Liberal Democrats than perhaps folks have been in the past few days," he said.
Mr Farron said the party needed a "fresh start", and said he wanted to speak to "members, councillors and activists" before deciding on his role.
Pressed on his intentions, he said he was "determined to play a big role" in making sure the party "survives and thrives".
In his resignation speech on Friday morning, Mr Clegg said the results were "immeasurably more crushing" than he had feared, saying it had been a "huge honour" to lead the party.
"It's simply heartbreaking to see so many friends and colleagues who have served their constituents over so many years abruptly lose their seats because of forces entirely beyond their control," he said.
One of the favourites to replace Nick Clegg as Liberal Democrat leader says he will decide whether to put himself forward "in the next few days".