An M&S spokesperson confirmed that the company is in talks with a number of different companies, but insisted that plans were "at a very early stage".
"We'll only do something when it's right for the business and the brand," the M&S spokesperson said. "We'll consider anything to enhance the site."
One report on Friday, in the Evening Standard, claimed that Amazon was lined up to take over the contract. M&S dismissed this claim as "a bit misleading", saying that no deal had been made with Amazon.
However, M&S refused to say which companies it is speaking to, or even what types of companies they are.
Amazon did not immediately respond to requests for comment. The company does have experience of working with other firms, such as Borders and Toys R Us.
The Toys R Us alliance hit rocky times, though, after Amazon.com began selling its own range of toys. Toys R Us launched a lawsuit claiming this violated the two firms' earlier agreement, and said that Amazon.com had violated Toysrus.com's "exclusive rights" to sell toys, games and baby products on the Amazon Web site. Amazon then countersued, and the case is ongoing.
The M&S's spokesperson claimed that the company's Web site performs pretty well compared to rival high street retailers, with a good ranking from traffic-tracking firm Hitwise.
M&S has been through some turbulent times in recent months. It repelled a takeover bid by retailing magnate Philip Green in July, but new chief executive Stuart Rose is under pressure to improve the firm's performance and get its share price higher.
Handing over the online operations to a specialist third-party could help Rose to concentrate on the performance of M&S' physical stores.