The paper launched a survey yesterday, which informed readers that it was considering charging $5 (£3) a month for its online content, including articles, blogs and multimedia.
It then asked: "How likely would you be to pay a $2.50 monthly fee -- which would be a 50% discount for home delivery subscribers -- for continued, unlimited access to nytimes.com?"
Catherine Mathis, New York Times Company spokeswoman, said that a monthly access fee was only one possibility being considered.
Mathis said: "The purpose of the survey is really to reach out to our home-delivery subscribers and understand how they would react to a pay model for the website.
"We are evaluating a variety of scenarios where access to our content, in varying amounts, would require a fee."
Nytimes.com, which is currently free, did previously charge an access fee for its premium content, such as opinion pieces and blogs, through an initiative called TimesSelect.
The TimesSelect service was launched in 2005, but shut down two years later.
The paper is now reportedly considering two payment models.
Scott Heekin-Canedy, president and general manager of The New York Times Media Group, told The Daily Telegraph that he was looking at the "metered" model, where users can access a certain number of articles before being charged, and the "membership" model, which would include access to premium content and services for those who pay a monthly fee.
However, micro payments will not be an option for The New York Times.
Heekin-Canedy told the Telegraph that the paper was not interested in micro payments -- charging users a small fee per news article or video clip -- saying that they would not work for newspaper websites.
He said: "Our general view is that micropayments are too cumbersome. It is just like getting in a taxi and the meter is running for every word or page you consumer.
"It creates an anxiety that just doesn't belong here."
Heekin-Canedy also said that a decision regarding the payment models would be made by the end of August.
The move would make The New York Times the first major non-financial newspaper group to take the step.
News Corporation's Wall Street Journal charges for access to some of its website's content, as does the Financial Times, which offers visitors some articles for free each month.
Last week Rupert Murdoch's News Corp launched a survey asking iPhone and Blackberry users if they would be willing to pay a subscription to access the mobile version of the Wall Street Journal, which is currently offered as a free application.
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