Sir Cable, who took over from Tim Farron after last year’s election, is due to give a policy speech on 7 September, a week before the party gathers in Brighton for its annual conference.
The Sunday Times and Business Insider both suggested that he would use the speech to announce plans to step down before the next general election, which is scheduled for 2022, when he would be 78 or 79.
They reported that he could also unveil plans to allow people to run for party leader if they are not an MP. The party currently has 12 MPs.
A party source told the Press Association: “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”.
Some parties have had leaders who are not among their MPs in Westminster.
They include current SNP leader Nicola Sturgeon, who is first minister in Scotland, and former Green Party leader Natalie Bennett, who stood unsuccessfully at the 2015 election.
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