Political experts see veteran Sir Vince as the obvious successor to Tim Farron.
Securing the leadership of his party would complete a remarkable return for Cable, who was rejected by voters in 2015 only to win his Twickenham back earlier this month.
Former health minister Norman Lamb has also indicated he is considering a bid for the leadership, but hotly tipped East Dunbartonshire MP Jo Swinson, 37, has ruled herself out, saying she will fight for the deputy leadership instead.
Writing on Liberal Democrat Voice, Sir Vince said: “I believe I can as leader offer the energy, dedication and drive, as well as experience, to help – with you – to make our party a credible contender for power”.
Former energy secretary Sir Ed Davey has also said he is giving “serious thought” to standing.
He described Brexit as an “iceberg” about to hit the United Kingdom economy and said the Lib Dems should “warn of the dangers ahead and the need for a new course”. He said there was big opportunity for his party with the Conservatives “in disarray” and Labour still lacking economic credibility.
Cable, 74, has perhaps the highest profile among the 12 Liberal Democrat members of the House of Commons.
Sir Vince said that there is a “big space in British politics” which he is “determined” for the Lib Dems to occupy.
If elected, Sir Vince would be the party’s oldest ever leader and the oldest leader of a major party since Sir Winston Churchill, who stepped down as Tory leader at the age of 80.
A source close to Cable’s campaign told IBTimes UK that they now have six supportive MPs.
“To be a political leader – especially of a progressive, liberal party in 2017 – and to live as a committed Christian, to hold faithfully to the Bible’s teaching, has felt impossible for me”, he said. He has previously served as Lib Dem deputy leader and interim leader while members selected Nick Clegg in 2007.