But The Australian quoted sources saying a consular office would be opened initially in Jerusalem because the cost of moving the embassy was estimated to be AU$200 million (£114 million).
After Mr Morrison came to power in August, he was invited by Prime Minister Benjamin Netanyahu to Jerusalem.
In a follow-up call with the Israeli PM, Mr Morrison said: "We're committed to a two-state solution, but frankly it hasn't been going that well, not a lot of progress has been made, and you don't keep doing the same thing and expect different results."
US President Donald Trump had sparked anger after announcing the US would recognise Jerusalem as Israel’s capital last December.
The US embassy moved from Tel Aviv to Jerusalem on May 14, a day marked by mass protest in the Gaza Strip, where about 60 Palestinian protesters were killed by Israeli fire in border clashes.
Guatemala followed suit, opening its own embassy in Jerusalem that same month. Brazil and the Czech Republic have announced their intention to move.
