The federal government is edging closer to a deal on its higher education changes before Christmas, says crossbench senator David Leyonhjelm.
The coalition needs six extra votes to get its university deregulation bill through the Senate.
The bill, which passed the lower house in September, has been listed as the first piece of business for the final sitting week of the Senate for 2014.
Senator Leyonhjelm says over the past week Education Minister Christopher Pyne had been "strenuously lobbying" both him and the crossbench.
"Christopher Pyne tells me he's pretty confident he's got the numbers," he told Sky News on Sunday.
"He seems to be fairly sure that he'll get something up."
It was reported on Sunday that Mr Pyne is manoeuvering to secure a five-year freeze on university loans for stay-at-home mums and dads and will also dump plans to hike university loan interest rates.
The proposed interest rate changes have been a primary concern of Family First's Bob Day.
"I'd like to move an amendment to knock that one out," he told Sky News.
"If we support each other's amendments, and chip away at it, perhaps it will get into a form that the crossbench will accept."
However the government is still struggling to win over the support Senator Jacqui Lambie, who has vowed to vote against all government legislation in the Senate until Defence personnel get a fair pay rise.
Senator Lambie said she was not satisfied by reports the government will concede ground on the Defence pay deal by reinstating Christmas leave entitlements.
"It's all or nothing on the ADF pay deal. I'm not going to take any prisoners. It's time to empty the magazine, fix bayonets and charge," she said on Sunday.
She was due to meet with Prime Minister Tony Abbott in Canberra on Monday, but that meeting was cancelled over the weekend, according to her office.
Senator Xenophon told AAP Senator Madigan's proposals had "merit", but he still wants the vote delayed until 2015.
The lower house will continue debating counter-terrorism laws on Monday.
Committee reports are due to be tabled in the Senate next week on the Manus Island detention centre, income inequality and public transport.
