Russian-Israeli billionaire Abramovich is on the hunt for his successor after almost two decades in charge at Stamford Bridge.
The move came amid increased scrutiny on Russian oligarchs in the UK due to Russia's invasion of neighbouring Ukraine.
But who is Abramovich's potential replacement Wyss and what has he said about taking over Chelsea? talkSPORT.com has all the details…
Who is Hansjorg Wyss?
The 86-year-old is a billionaire businessman from Switzerland.
Born on September 19, 1935 in Swiss capital Bern, Wyss made his fortune through Synthes.
Synthes is a company he founded in the 1970s which manufactures medical devices - e.g. internal screws and plates for broken bones.
Wyss has a master's degree in civil and structural engineering at the Swiss Federal Institute of Technology in Zurich while he also obtained an MBA from Harvard's Business School.
He has been based in the U.S. since the 1960s and throughout his career has also worked in the steel industry and sold aircraft as a side business.
Wyss sold Synthes to Johnson and Johnson in 2012 and his net worth was estimated at $5.1 billion (£3.8bn) in 2022, according to Forbes.
The American business magazine has also labelled him as "among the most philanthropic people in the world" for his charitable donations.
The Wyss Foundation was set up back in 1998 as an environmental protection project and has worked with the likes of Leonardo Di Caprio.
What has been said?
Speaking to Swiss newspaper Blick, the 86-year-old said: "Abramovich is trying to sell all his villas in England.
"He also wants to get rid of Chelsea quickly. I and three other people received an offer on Tuesday to buy Chelsea from Abramovich.
"I have to wait four to five days now. Abramovich is currently asking far too much. You know, Chelsea owe him £2 billion. But Chelsea has no money.
"As of today, we don't know the exact selling price. I can well imagine starting at Chelsea with partners. But I have to examine the general conditions first.
"What I can already say: I'm definitely not doing something like this alone. If I buy Chelsea, then it would be with a consortium consisting of six to seven investors."