Republican Sen. Chuck Grassley is turning to Democratic House Speaker Nancy Pelosi for help selling his bipartisan bill to lower drug prices in the Senate.

Grassley told CNBC on Tuesday that he wants to persuade Pelosi to abandon her drug pricing bill, passed by the House in December, and support his legislation. He argued that there's "no other bill that can get the 60 votes required" to pass the Senate. The Iowa senator said Pelosi's bill, which would allow the government to negotiate lower prices for certain drugs, does not stand a chance in the GOP-controlled upper chamber.

Pelosi's support would put "pressure on the leadership of the United States Senate to get our bill up," Grassley said on "Squawk Box." "The president supports it. We have bipartisan support in the Senate."

A spokesman for Pelosi's office did not immediately respond to a request for comment.

Grassley, chairman of the Senate Finance Committee, worked with ranking Democrat Ron Wyden of Oregon to pass a broad drug pricing bill through their committee in July. High prescription costs have become a rare bipartisan issue. Health care remains a top issue for voters ahead of the 2020 election.

Grassley's bill would make changes to Medicare by adding an out-of-pocket maximum for beneficiaries and capping drug-price increases at the rate of inflation, among other measures. The bill has stalled due to lack of support from Senate Republicans.

Senate Majority Leader Mitch McConnell of Kentucky has not scheduled the bill for a vote.

Grassley last month accused him of sabotaging it. During a briefing with reporters on Dec. 18, Grassley said that "the president wants it" but more Republicans don't support it because McConnell "asked them not to."