Mr Rennie wants the SNP administration to extend its free childcare proposals to cover 40% of Scotland's two-year-olds, starting with the most vulnerable children.
First Minister Alex Salmond announced in January that from August this year every two-year-old from a ''workless'' family will be entitled to 600 hours of free childcare, representing 15% of two-year-olds.
From August next year free childcare provision will be extended further, reaching 27% of all two-year-olds, by widening the entitlement to families who receive certain welfare benefits such as income support.
Mr Rennie is expected to tell his party's Spring conference in Aberdeen: "Thanks to the UK budget and the improving economic conditions the Scottish Government now has the money they need to implement the childcare package in full.
"I want John Swinney to use the extra money he has received in that budget to fully match the excellent work south of the border on early education and childcare.
"He should make a statement to parliament next week that he has agreed to this extension.
"He's just over half way there already. Now he's got all the money necessary he can travel the whole way.
"No fuss, no groaning, just do it. Future generations will thank us for this."
The conference will also hear from Scottish Secretary Alistair Carmichael, who will say that a "a No vote will deliver real freedom" and "unplug the constitutional blockage and open the way to real progress for people".
He is expected to tell delegates: "At its best this referendum can be cathartic for Scotland.
"It can clear the air. A positive vote to stick with the UK family will not only provide certainty and stability for Scotland.
"It will unplug the constitutional blockage and open the way to real progress for people.
"No more arguing over numbers and projections but real freedom to innovate and improve people's lives.
"For all that the SNP may hate it, Scotland is striding forward right now as part of the UK."
He will add: "Thanks to the Scotland Act, the Scottish Parliament will have new powers to set income tax, borrow to invest and to innovate in far-reaching ways.
"We need the debate to begin on how those powers will be used.
"We need to start talking again about how we improve healthcare and education and the environment here in Scotland.
"And we need the Scottish Parliament to empower our democratically elected local governments.
"Increasing their financial powers, paving the way for greater community action, and introducing clear powers of general competence.
"A law that would entrench the role of local councils and compel Scottish governments to uphold it.
"We need these things to happen. We need a No vote to enhance Scotland, improve Scotland and move on."