They were attracted to the high sales of treadmills and exercise bikes from Peloton during the pandemic.
The return to gyms after lockdown has not put off the company's customers, which has now been valued at less than half of its peak value of $50bn.
Recent PR disasters include heart attacks in TV stars who were using Peloton machines.
Amazon declined to confirm whether or not it was considering an offer for the US manufacturer of exercise equipment.
After the Wall Street Journal reported the rumour, shares of the firm surged more than 30% during after-hours trading.
The Financial Times reported the first time that Nike had decided to pursue a deal.
A spokesperson for Amazon stated that they don't comment upon speculations or rumours. Peloton and Nike didn't immediately respond to requests for comment.
This once-favorite stock market favorite has seen its shares plummet in recent months, losing over 80% of its value in just one year.
Peloton's share price rose after the Covid pandemic caused gyms to close in 2020.
However, the demand for treadmills and bikes has declined as lockdowns have made it easier to get them.
The firm reduced the price of its flagship bike 20% to $1,495 (PS1,105) in August as it disclosed that its losses were increasing and its revenue growth was slowing.
The US Department of Justice, and the Department of Homeland Security announced that they were looking into the company following the death of a child who was allegedly pulled under one of the treadmills. Other customers had also reported injuries.
Peloton informed investors in November that revenue would slow in the coming year.
It stated in a letter to shareholders that "the primary drivers of our reduced outlook are a more prominent tapering of demand related the continuing opening of the economy and a richer mix of sales to the original bike."
Blackwells Capital, an investment firm, demanded that John Foley, Peloton's chief Executive Officer be fired and that the company be sold.
Blackwells stated that Peloton and its customer base "extremely appealing" to companies such as Nike, Apple, Disney, and Sony who are looking to increase their presence in the home and health, wellness, and media space.
Wedbush Securities analysts also believe that other bidders will emerge. They stated that they would be surprised if Apple did not get involved in the potential deal process.
"We believe that there will be a few technology and consumer brand stalwarts looking for a bid, with activists pushing for a sale."
Peloton was recently in the news after two TV dramas: the Sex and the City Revival. Just Like That and Billion featured stories where characters had heart attacks while riding their bikes.
On Tuesday, the company will publish its second quarter results.