The veteran independence campaigner also says there should not be another independence referendum for at least five years to allow Nationalists to reframe the case for a Yes vote.
Mr Sillars criticised Ms Sturgeon's judgement in pushing for a second referendum after the Brexit vote, insisting it caused the loss of 21 seats which the party suffered in this year's Westminster election. The party still won 31 of Scotland's 59 seats.
"She's the only one we've got at the present time," Mr Sillars said on BBC Scotland's Politics Show today when asked if Ms Sturgeon should remain as leader.
"Suppose Nicola was knocked over by a bus this afternoon where are the candidates of the necessary stature to take over the leadership of the SNP?
"She's what we've got at the present time and I would like to see her improve."
He added: "If there was someone better around who had the intellectual capability to understand that you've got analyse things first before you take a decision, yes I think she should step aside.
"But there's no-one there at the moment."
Ms Sturgeon has indicated a second referendum is likely before the end of the current Parliament n 2021, but Mr Sillars said this is premature.
"I'm for a second independence referendum but you cannot actually have one sensibly until you know exactly what the Brexit deal is in detail and then take time to assess it and take time to actually formulate an argument for independence.
"We're in a new paradigm
"What was in 2014 will no longer be the case after Brexit, so we have to have a new thinking of the structure which we put to the Scottish people."
A "post-mortem" is needed on the reasons for defeat in the first referendum, he said, or the Yes side will lose again.
He added: "You're probably '22/'23 before you actually have the referendum."
This could mean the pro-independence majority is lost at the Scottish Parliament which would derail the prospect of a vote happening.