Israel must also be able to assure its Arab neighbour that "justice has been served" in the case, the source added.
The embassy was closed shortly after Israel hastily repatriated the guard under diplomatic immunity to prevent Jordanian authorities from interrogating him and taking any legal action against him. The Israeli ambassador and embassy staff were pulled out.
Israeli sources said on Wednesday they were planning to replace Ambassador Einat Schlein at the Amman embassy in an effort to improve ties. However they did not address the long-standing Jordanian demand to take legal action against the security guard.
"They can look for a new ambassador but that ambassador will not be welcome in Jordan until a due legal process takes its course and justice is served," the diplomatic source said.
"Our position remains solid in Jordan.. The embassy will not reopen until these conditions are met... which is the position we took from the very beginning," he added.
Jordanian officials have treated the shooting as a criminal case and say the two unarmed Jordanians, one a bystander and the other a teenage workman, were killed in cold blood by the armed guard.
Israel said the armed guard opened fire after being attacked and lightly wounded by the workman who was delivering furniture at his home within the embassy compound and acted in self- defence, in what Israeli officials called a "terrorist attack".
The handling of the shooting has tested ties between Israel and Jordan, one of only two Arab states that have a peace treaty with Israel. They have a long history of close security ties.
Israel has said it is highly unlikely it would prosecute the security guard but has hinted at financial compensation to the family of one of the dead Jordanians.
Protesters chanting slogans during a demonstration near the Israeli embassy in Amman, Jordan, on July 28, 2017.
Jordan will not allow Israel to reopen its embassy in Amman until it has launched legal proceedings against an Israeli security guard who shot dead two Jordanian citizens in July, a Jordanian diplomatic source said on Thursday.
