Independent Democratic Conference Leader Jeff Klein on Tuesday left the door open to adding more money to the Senate’s one-house budget bill when it comes to universal pre-Kindergarten spending.

At the same time, Klein indicated that Gov. Andrew Cuomo’s statewide proposal doesn’t fully fund the plan.

“Right now what the governor proposed is $100 million for pre-K,” Klein, the Senate co-president, told reporters after addressing labor members in Albany. “Mayor de Blasio wants $300 million. It’s not enough even for the first year.”

Cuomo’s proposal would fund universal pre-Kindergarten at $1.5 billion over five years. In the coming 2014-15 budget year, $100 million would spent, with $100 million added each year.

The governor’s budget would direct the money to the neediest districts first.

But lawmakers, as well as advocates for the pre-K plan, the spending proposal won’t cover the full state even when it is implemented in the fifth year.

State Education Commissioner John King has said spending for pre-K statewide would cost $1.6 billion annually.

Supporters of the de Blasio approach want a “dedicated funding stream” — which for now includes a tax on the wealthy in New York City.

As for adding more money to the proposal, Klein didn’t rule that out.

“That’s something we have to look at,” he said. “I’m still looking at making sure we have a dedicated funding stream, that the money is there. That’s why I support de Blasio’s tax.”