A Sunday Times spokeswoman confirmed that the section's future is being reviewed over the next few months.
"We are looking at all the options, including going online," she said. She did not deny that the options included axing the print section.
News International owns the domain name fundaytimes.co.uk, but the site only contains links to the company's newspaper brands. There is also no mention of Funday Times on timesonline.co.uk.
Funday Times has been a part of the paper since 1988 and has outlasted other children's supplements launched by The Daily Telegraph and The Independent. It employs five staff including editor David Coombs.
The paper has been redesigned in recent years, with a major overhaul just over a year ago. The move shifted the appeal of the title to the older teen market by dropping its front-page cartoon in favour of a lead feature and celebrity interview.
The idea was to make it look similar in style to teen magazines such as Sugar and Smash Hits with a greater prominence on celebrity gossip and interviews with boy bands like McFly. However, it is not believed the move has been a success in terms of attracting advertisers.
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