Up to six ministers are reportedly set to be bumped from the Federal cabinet in a major reshuffle, but under siege treasurer Joe Hockey is not one of them.

Tony Abbott is planning on axing a handful of Howard-era ministers in favour of MPs elected post-2007, the Daily Telegraph has reported.

Senate leader Eric Abetz, Defence Minister Kevin Andrews and Industry and Science Minister Ian Macfarlane are tipped to be tapped on the shoulder.

Ian Macfarlane and Kevin Andrews. (AAP)

Prime Minister Tony Abbott and Senator Eric Abetz. (AAP)

But Mr Hockey retains the support of the prime minister despite a series of gaffes and unpopular budgets, the newspaper reports.

Education Minister Christopher Pyne dismissed the rumours.

"All of the people you have mentioned are good men doing a good job," he told TODAY.

Christian Porter, Marise Payne, Kelly O'Dwyer, Michaelia Cash, Dan Tehan and previously demoted backbencher Arthur Sinodinos are tipped to climb the ladder.