The Islamic State (IS) group overran the city dubbed the "Pearl of the Desert" last May, and it has since blown up UNESCO-listed temples and looted relics dating back thousands of years.
Its recapture would be a strategic as well as symbolic victory for President Bashar al-Assad, since whoever controls it also controls the vast desert extending from central Syria to the Iraqi border, experts say.
Loyalists backed by Russian air strikes were "800 metres (yards) from Palmyra" and now control areas linking the city to Damascus and third city Homs, a Syrian security source said.
"The army is now at (the southern and southwestern) entrances to the city and is preparing to begin the battle to liberate Palmyra," the source told AFP.
Rami Abdel Rahman of the Syrian Observatory for Human Rights said earlier Wednesday that regime forces were two kilometres (little more than one mile) south of Palmyra and five kilometres southwest of the city.
In Geneva, meanwhile, negotiators were making a fresh bid for a breakthrough ahead of a planned pause in the peace talks starting Thursday.
There is some hope that high-level US-Russian meetings this week could deliver the momentum needed to move on to a new round.
US Secretary of State John Kerry arrived in the Russian capital ahead of meetings on Thursday with President Vladimir Putin and Foreign Minister Sergei Lavrov, with Syria a key issue on their agenda.
With the indirect negotiations in Geneva proving to be sluggish, all eyes are on Moscow since the two powers hold significant sway over the opposing sides in Syria's devastating conflict.
- 'Interconnected' -
"The diplomatic process in Geneva is interconnected with what is taking place in Moscow," said the High Negotiations Committee, the main opposition umbrella group.
The HNC said it hoped that after the Kremlin talks "a clear message will be sent to Bashar al-Assad: He cannot continue to paralyse the political transition that the Syrian people are demanding.
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"Syria's future must be decided by the Syrian people, not by a single man," said the group, whose leader Riad Hijab -- a former prime minister who defected in 2012 -- was set to hold a first official meeting with UN envoy Staffan de Mistura on Wednesday.
Assad's fate has been a key obstacle in the latest talks, with the government stubbornly insisting any discussion of him leaving is "excluded" and the opposition saying any talk of allowing him to stay is "absolutely unacceptable".
De Mistura meanwhile voiced "a strong expectation that the talks in Moscow will be productive."
When the two powerful ministers reach a "common understanding", the process is helped "enormously", said the envoy, who was also due to meet with EU foreign policy chief Federica Mogherini later Wednesday.
Washington and Moscow were instrumental in bringing about a partial, fragile ceasefire declared on February 27, raising hopes for an end to the five-year Syrian conflict that has killed more than 270,000 people and forced millions to flee their homes.
- Aid delivery 'green light' -
The ceasefire does not include areas held by IS and Al-Qaeda-linked Al-Nusra Front, allowing the regime to launch an offensive at the start of the month, backed by heavy Russian air strikes, to try to retake Palmyra.
Moscow, which made a surprise announcement last week that it was withdrawing most of its troops from Syria, has continued support for the government's bid to liberate what Putin described as a "pearl of world civilisation".
Russia's military intervention in Syria from September at Assad's request has already allowed the regime to retake significant territory it had lost to various armed opposition groups.
But experts say Moscow's partial withdrawal could help the peace drive by weakening Assad's position.
"If the Russians drop Bashar, he will collapse," said Middle East consultant Agnes Levallois.
But the regime's lead negotiator for the Geneva talks, Bashar al-Jaafari, insisted that thinking Moscow could pressure its historic ally in Damascus was a "misreading" of the situation.
"When we say that the dialogue must be between Syrians, without outside intervention, this also applies to the Russians and Americans," he told AFP.
The UN said meanwhile that the Assad regime has given "a verbal green light" for it to make deliveries of humanitarian aid to 15 of 18 besieged areas in desperate need of life-saving supplies.