But success in the upcoming election will not prevent him from retiring next year.
Sir Malcolm, who is also the chairman of the House of Commons International Development Select Committee, said that he still intended to stand down as an MP at the 2015 general election.
It is thought a number of senior party members approached Sir Malcolm to ask him to throw his hat in the ring to be deputy leader.
His main opponent is Solihull MP Lorely Burt.
Her supporters say the high-profile job could help her hold onto her marginal seat in 2015. A number of her backers are also thought to believe her election would help the party at a time when it faces claims it has a problem with women.
But Sir Malcolm has been described by his supporters as "experienced and strong and a safe pair of hands". It is understood that they feel that could be particularly important in the run up to what is expected to be a difficult election campaign.
"It would be a privilege to serve my party if I am elected," Sir Malcolm said.
The contest was triggered by former deputy leader Simon Hughes's decision to resign the post to become a justice minister.
Sir Malcolm will have spent 32 years representing the people of Gordon when he stands down next year.
Announcing his retirement plans, he said that he wanted to "go while I'm still fit, active, effective, I hope, and enjoying it, rather than when I'm jaded and tired".