The massive change would replace the current reverse-chronological feed so beloved by current users who complain the social media site is becoming just like Facebook.
Twitter has yet to confirm the new but there are reports it will be an opt-in option.
#RIPTwitter was trending worldwide on Saturday morning with people voicing their despair at the transition.
Twitter was created in March 2006 by Jack Dorsey, Evan Williams, Biz Stone, and Noah Glass and quickly became one of the world's most popular social media tools and now has over 320 million active users.
The current format allows for all tweets from people a person follows to be displayed in their timeline as well as options for custom lists.
An algorithmic timeline would allow for Twitter to bring what it deems more popular content to feature more prominently.
Twitter CEO, Jack Dorsey, said in July: "We continue to show a questioning of our fundamentals in order to make the product easier and more accessible to more people."
There have already been rumours the company my remove the 140 character limit on tweets.