Saleh reportedly told a meeting of senior officials, military leaders and tribal chiefs that he would not hand over control of the Arab nation to the military once he quits.
The move appeared to be a reversal of his earlier rejection of an opposition proposal demanding such a resignation.
However, it was not immediately clear if protesters, who have been camped out around the university in the capital Sanaa for weeks, would accept the latest offer after more than 50 of them were shot dead on Friday.
Saleh's support has been draining away since the killings were carried out by plainclothed snipers.