The two countries re-established relations in January 2021, after the UAE took part in a nearly four-year Gulf blockade of Qatar, but despite several meetings they are yet to restore the diplomatic missions.
"Regarding the opening of embassies between the two countries, I think it will be in the coming weeks," Qatari foreign ministry spokesperson Majid Al-Ansari told a briefing.
"The technical committees are now doing their work in this context, and it is expected that there will be exchange visits to consider the procedures we need to reopen embassies."
A UAE official confirmed that the reopening of embassies is "under process".
"At present, the activation of diplomatic ties, which will include the reopening of embassies, is under process between both countries," the official said in a statement sent to AFP.
Opening the embassies would be just the latest in a series of reconciliatory steps for Gulf relations since heavyweights Saudi Arabia and Iran moved to restore ties last month.
Last week, Qatar put aside a chronic feud to resume relations with Bahrain. The two sides aim to quickly reach the "highest levels of cooperation", Al-Ansari said on Tuesday.
Saudi Arabia has been negotiating a fresh ceasefire in Yemen's civil war and nearly 1,000 prisoners from the conflict, pitting a Saudi-led coalition against Iran-backed Houthi rebels, have been released in recent days under an exchange deal.
In further evidence of the mood of détente, Saudi Arabia's top diplomat was expected in Damascus on Tuesday, the first such visit since the start of Syria's civil war in 2011.
Saudi Arabia, the UAE, Bahrain and Egypt imposed a diplomatic and transport blockade on Qatar in 2017, accusing it of supporting extremist organisations in the region and becoming too close to Iran. Doha strongly denied the allegations.
A reconciliation accord was sealed in January 2021. The UAE and Qatar held one of a series of meetings earlier this month in what the Qataris called a "positive atmosphere".
Saudi Arabia and Iran's decision to resume ties appear momentous because they have long been vying for influence around the region, backing opposing sides in conflicts including Yemen.
Analysts say Saudi Arabia, the world's biggest oil exporter, is now seeking to calm Gulf tensions and focus on ambitious domestic projects aimed at reducing its economic dependence on crude.