Mengistu, called the "Butcher of Addis Ababa" by his enemies, was driven from power in 1991. He was sentenced to death in absentia last year.
Zimbabwe’s opposition Movement for Democratic Change (MDC), which has agreed to join a government with Mugabe, said it would seriously consider extraditing Mengistu if it were forming a government by itself.
"But what we are going to have is a government of national unity, and decisions there will have to be reached through some consensus and I don’t know whether that’s going to be possible," said MDC spokesman Nelson Chamisa.
The extent of the MDC’s influence in the new administration remains unclear.
The Ethiopian government has long called for Mengistu’s extradition, but Mugabe’s government has refused that.
He was sentenced to death in absentia in May 2008 by Ethiopia’s Supreme Court. It found him guilty of genocide arising from the thousands of killings during his 17-year rule that included famine, war and the "Red Terror" purges of his suspected opponents.
Yoseph Kiros, the special prosecutor during the trial of Mengistu and other senior officers, welcomed any chance that prospects for extraditing Mengistu could have improved. He said any such decision by Zimbabwe "would bestow great honour on that country."