That faction wants to put Cruz on the Supreme Court instead - which would rule the senator out of another tilt at the White House

Meanwhile another group of billionaires wants Kansas Secretary of State Kris Kobach, who has a hard-line approach to immigration

Two separate factions are facing off over who lands the Attorney General job in the Donald Trump administration

A fight is brewing among forces behind the Trump transition over the future of the Justice Department, with separate factions pushing Texas Sen. Ted Cruz and Kansas Secretary of State Kris Kobach.

A cabal of wealthy Texas oilmen is aggressively promoting Cruz for attorney general, according to a person with direct knowledge of discussions behind the scenes who also said the one-time Trump rival wants the slot.

On Thursday a new wrinkle emerged, with the Trump transition team releasing a statement about a meeting between Trump and Alabama Sen. Jeff Sessions.

Trump, the statement said, 'has been unbelievably impressed with Senator Sessions and his phenomenal record as Alabama's Attorney General and U.S. Attorney.' Those words suggest he is being considered to run the Justice Department.

A separate group of billionaires is encouraging the president-elect's team to embrace Kobach, citing his hard-line approach to restricting immigration across the board.

Those insiders want Trump to appoint Cruz to the U.S. Supreme Court instead.

Scroll down for video

A cabal of wealthy Texas oilmen is aggressively promoting Cruz for attorney general, according to a person with direct knowledge of discussions behind the scenes

A separate group of billionaires is encouraging the president-elect's team to embrace Kansas Secretary of State Kris Kobach, citing his hard-line approach to restricting immigration across the board

'There's a good argument to be made that Sen. Cruz would be the best Supreme Court justice the administration could appoint,' a transition insider said Thursday.

That outcome, however, would require him to sacrifice his political ambitions, including a possible second run for the White House in the future.

It would also open up Trump to accusations of backpedaling on a pledge to appoint Supreme Court justices only from a list of 21 candidates he touted during the campaign.

The president-elect vacillated this year between vowing to restrict himself to that list and promising only that it was a 'list that I would either choose from or pick people very close in terms of the spirit and the meaning of what they represent.'

Cruz's name was not among those he released.

Meanwhile Leonard Leo, executive vice president of the conservative Federalist Society, told reporters Wednesday that he expects Trump to stick to his list.

'My understanding from our discussion today is that is still the list, and that he is committed to evaluating those people very carefully, honing that list and then ultimately making a nomination upon his assumption of the office,' he said.

Cruz and Trump together in Washington in September last year. Trump excoriated his rival as 'Lyin' Ted' on the campaign trail - but he could still be in line for top jobs in the President Elect's new administration

It's unclear whether Trump will appoint Cruz to fill either position. He excoriated him as 'Lyin' Ted' on the campaign trail, retweeted and unflattering picture of Cruz's wife and suggested that Cruz's Cuban-immigrant father was linked to John F. Kennedy's assassination.

But GOP leaders in the Senate hope Cruz will exit Capitol Hill one way or another, an aide to a senior Republican there said Wednesday.

The aide cited Cruz's 'bull in a china shop' reputation in Congress and his eagerness to put up roadblocks to moderate legislation in the name of conservative principles.

Cruz had trouble recruiting fellow senators to back his White House run, with some privately carping about his 21-hour filibuster that threatened to shut down the federal government over a budget that included funding to keep the Obamacare system afloat.

Senators who disagreed with him, he said during his marathon speech, were akin to 'Neville Chamberlain, who told the British people, "Accept the Nazis".'

South Carolina Sen. Lindsey Graham told reporters Tuesday that he had 'added a name to the list: Senator Cruz.'

'I think he’d get a lot of votes,' Graham said.

The group of Texas money-men, according to the Trump transition insider, hope an Attorney General Cruz would reverse the Obama administration's intensified antitrust oversight of oil and gas drilling and leasing.

They want Cruz to call off the dogs, opening a wider lane for the kinds of joint ventures and collaboration among energy exploration competitors that were once commonplace in the industry.

They also want to see Dallas financier and Trump Victory Committee vice-chairman Ray Washburne appointed to lead the Department of the Interior.

Washburne was seen entering Trump Tower on Thursday.

'It's all about wanting "drill, baby, drill",' the insider said, referring to fossil fuel interests' desire to see the Trump administration scrap President Obama's slow-walk of drilling and fracking leases.

Cruz played coy Thursday morning on 'Fox & Friends,' saying he has 'an incredible job right now representing 27 million Texans' but also not shutting the door on becoming the next attorney general.