Wyss, 86, who founded the medical device manufacturing firm Synthes, told the Swiss newspaper Blick that he and three others had been sounded out on Tuesday.
But Wyss wants Abramovich to lower his asking price for the English Premier League side.
Abramovich revealed Saturday that he plans to place his ownership of the Blues into the “stewardship and care” of the Chelsea Foundation’s trustees.
Abramovich has not been named on a growing British sanctions list targeting Russian banks, businesses and pro-Kremlin tycoons in the wake of Moscow’s invasion of Ukraine.
But British Prime Minister Boris Johnson has been pressed on why Abramovich has not been cited, given his familiarity with Russian President Vladimir Putin.
“Abramovich is among Putin’s closest advisers and friends,” Wyss told Blick.
“Like all the other oligarchs, he is panicked. Abramovich is currently trying to sell all his villas in England. He also wants to get rid of Chelsea quickly. Along with three other people, I received an offer on Tuesday to buy Chelsea from Abramovich.
“I have to wait four or five days. Abramovich is asking too much right now. Chelsea owes him £2 billion ($2.7 billion, 2.4 billion euros). But Chelsea has no money. This means that those who buy Chelsea must compensate Abramovich.
“We do not yet know the exact sale price. I can very well imagine myself joining Chelsea with partners. First I have to look carefully at the conditions.
“I certainly wouldn’t do such a thing alone. If I buy Chelsea, it will be with a consortium of six to seven investors.”
Johnson was asked in Warsaw on Tuesday why Abramovich has not been personally sanctioned by Britain, as several UK lawmakers have demanded.
In response, Johnson did not mention the Chelsea owner, but said Britain would be “tightening the economic noose” further around the Russian regime.
In parliament on Tuesday, opposition Labour lawmaker Chris Bryant said Abramovich seemed “terrified of being sanctioned, which is why he’s already going to sell his home”.
Wyss praised the West’s “excellent approach” in imposing sanctions on Russian interests.
“The fact that the Russian oligarchs are targeted by the Americans and Europeans is absolutely essential, because they may have an influence on Putin,” he told Blick.