He is expected to make the announcement on 7 September ahead of the party’s conference in Brighton.
Sir Vince is also expected to announce proposals, which will be debated within the party, to introduce a new category of registered supporter similar to the one that allowed 180,000 people to vote in the Labour leadership elections.
He also proposes a change in the rules so supporters need to be enrolled for 12 months before voting, to prevent infiltration by rival parties.
But a Liberal Democrat source said Sir Vince, who replaced Tim Farron after last year’s election, was not using the speech to stand down.
The source said: “There are no plans to step down any time soon.”
The party currently has 12 MPs. Sir Vince’s deputy, Jo Swinson, is currently on maternity leave but is regarded as a potential future successor, as is Layla Moran, the party’s education spokeswoman.
However, a party source denied the rumours, saying: “He’s not about to stand down, or use the speech to stand down. There are no plans to step down any time soon.”
They also said that the idea of allowing a non-MP to be party leader is “not set in stone, but it’s an option”.
The package of reforms under consideration by the party is reported to have been partly inspired by Justin Trudeau’s Liberal party in Canada, which went from third place to victory in 2015.
Normal Lamb, the Liberal Democrat’s health spokesman told Sky News: “When you have a small parliamentary party, it inevitably limits the choice very considerably.
“You’ve got 12 people, some of whom won’t have any interest in being leader, or seen in that light, so you end up with a very small field potentially.
“And there may be other dynamic people out there beyond the parliamentary party who could have a significant impact on the future of liberal progressive politics, so why exclude them?”
The Lib Dem leader said engaging members and a wider body of supporters in selecting their leader and candidates had been crucial to their rise.
In his spring conference speech this year, he said: “I am determined that we Liberal Democrats should lead a new groundswell for political renewal.
“Our sister Liberal Party in Canada, under Justin Trudeau, leapt from third to first in a ‘first past the post’ system every bit as unforgiving as ours.
“I have turned to them for advice on modernisation on how we can apply their successful model here.”
A consultation on the changes is expected to last several months.