U.S. Senate Majority Leader Harry Reid, D-Nev., will offer a compromise on Monday to extend a popular payroll-tax cut, a fellow Democrat said Sunday.

Appearing on the Fox News Sunday program, Sen. Kent Conrad, D-N.D., said Reid's proposal would cover the cost of extending the tax cut, set to expire at the end of this month, but he left it to Reid to provide details on Monday.

The Democratic-controlled Senate last week defeated competing payroll-tax cut extension plans by Democrats and Republicans, showing the need for the two sides to find common ground.

Conrad, chairman of the Senate Budget Committee, said Reid told him during a phone conversation on Saturday that he would offer on Monday a compromise plan to extend the payroll-tax cut.

Conrad said Reid's plan will be a serious attempt to move this ball forward because we should not have a tax increase on the middle income [segment]. That just makes no sense in this economy.

In a pair of Senate votes last Thursday, Republicans and Democrats said no to each other's plans.

Republicans objected to Democratic calls to slap a new tax on those making more than $1 million to cover the projected $110 billion cost of extending the payroll-tax cut.

And Democrats rejected the Republican proposal to pay for it by extending a pay freeze on federal workers and reducing the federal workforce.

Conrad said Reid's plan would represent a compromise.

Although Conrad declined to release any details, he said Reid's proposal would be fully paid for and not increase the nation's record $15 trillion debt.

It will be paid for, it will be in a way that is credible and serious, Conrad said.

(Reporting by Thomas Ferraro; Editing by Paul Simao)