State Secretary Yusril Ihza Mahendra said Yudhoyono discussed the possibility of appointing army chief General Ryamizard Ryacudu as commander of the armed forces commander with parliamentary leaders.
Ryacudu, who was also the choice of Yudhoyono's predecessor Megawati Sukarnoputri, would replace Endriartono Sutarto.
Days before the end of her term, Megawati had approved Sutarto's resignation and asked parliament to appoint Ryacudu as the new military chief.
Yudhoyono, who became leader on October 20, withdrew Megawati's letter of request which parliament had yet to approve.
Yudhoyono, himself a former general, faces an opposition-dominated parliament and some 20 legislators have signed a petition asking him to explain his decision to retain Sutarto.
But Mahendra said Yudhoyono, known as SBY, could still name Ryacudu.
"It was also discussed that SBY may propose the same candidate to replace the current commander," Mahendra said Friday after a meeting between parliament leaders and Yudhoyono.
It was not clear when a new military chief would be named but Ryacudu's appointment would likely spark controversy.
He has made several controversial remarks in the past, including last month when he alleged that an "alarming" number of intelligence agents had infiltrated Indonesia to destabilize the country.
He has also described seven soldiers who were jailed for killing a separatist leader who sought peaceful independence for Papua province as "heroes".
Sutarto tendered his resignation earlier this month, saying he wanted to see fresh blood in the military. Earlier reports said he quit because he opposed Megawati's decision to award two retired generals in her cabinet honorary rank promotions.
The outgoing military chief is seen as a straightforward general who believes the military should be placed under civilian control. Under the rule of dictator Suharto, which ended in 1998, the military was heavily involved in politics.