The Chelsea FC owner – who has now recovered – reportedly suffered sore eyes and skin peeling.
Two Ukrainian peace negotiators were also said to have been affected.
The Wall Street Journal reported claims the alleged poisoning was orchestrated by hardliners in Russia who wanted to sabotage the talks.
A source close to Mr Abramovich told the BBC he had suffered symptoms of suspected poisoning. They said he had now recovered and was continuing with negotiations to try and end the war in Ukraine.
Earlier on Monday, Mr Umerov tweeted that he was “fine” and urged people not to trust “unverified information”.
The incident casts light on Mr Abramovich’s reported role as a broker in talks between Ukraine and Russia. The exact nature of his position is unclear, but a spokesperson for the oligarch has previously said his influence is “limited”.
On Sunday, President Zelensky said Mr Abramovich had offered him help to de-escalate Russia’s invasion of the country.
The Russian billionaire travelled between Moscow and Kyiv for several rounds of talks at the start of the month. He reportedly met President Volodymyr Zelensky during the trip, but the Ukrainian leader was not affected and his spokesman had no information about the incident.
The investigative journalism group Bellingcat said Mr Abramovich and the negotiators suffered symptoms “consistent with poisoning with chemical weapons”.
The symptoms included “eye and skin inflammation and piercing pain in the eyes”, Bellingcat reported.
Meanwhile, an unnamed US official was quoted by Reuters as saying that intelligence suggested the sickening of the men was due to “environmental” factors, not poisoning.
Mr Abramovich has since been seen in public, being pictured at Israel’s Tel Aviv airport on 14 March.
The conditions of Mr Abramovich and the Ukrainian negotiators, who include Ukrainian MP Rustem Umerov, have improved since the incident on 3 March, the paper quoted sources as saying.
Mr Abramovich was sanctioned by the EU and UK earlier this month over his alleged links to Russia’s President Putin, which he denies.
But Mr Zelensky has reportedly asked the US to hold off from sanctioning Mr Abramovich, arguing he could play a role in negotiating a peace deal with Moscow.
The Kremlin has said Mr Abramovich played an early role in peace talks but the process was now in the hands of the two countries’ negotiating teams.