The British billionaire, who owns Ineos and is a United fan, was unsuccessful in his bid to buy Chelsea in May and has now turned his attention to the Red Devils, the PA news agency understands.
The news comes after a report in Bloomberg said the Glazers are contemplating selling a minority stake in the club.
Radcliffe recently tried to buy Chelsea, with his late offer being rejected as Todd Boehly was successful in taking over from Roman Abramovich.
A spokesperson for Ineos said the company would be interested in purchasing a smaller stake with a view to eventually buying the club.
“If something like this was possible, we would be interested in talking with a view to long-term ownership,” an Ineos spokesperson said in the Times.
“This is not about the money that has been spent or not spent. Jim is looking at what can be done now and, knowing how important the club is to the city, it feels like the time is right for a reset.”
Ineos is interested in growing its sporting portfolio as it already owns French Ligue 1 side Nice and Swiss team FC Lausanne-Sport. It also sponsors the cycling team Ineos Grenadiers, which was formerly Team Sky.
The Glazers are hugely unpopular with United fans, who are unhappy at the club’s ownership model and declining performances on the pitch, having not won a Premier League title in nine years. The supporters regularly protest against them.
Manchester United did not comment on the story.
It comes on the same day that Elon Musk joked about buying the club.
The Tesla founder, who is a billionaire, made reference to United in a tweet.
Musk wrote: “To be clear, I support the left half of the Republican Party and the right half of the Democratic Party!
“Also, I’m buying Manchester United, ur welcome.”
He later clarified that “This is a long-running joke on Twitter. I’m not buying any sports teams. Although, if it were any team, it would be Man U. They were my fav team as a kid.”