Disney is working with a financial adviser to evaluate a possible bid according to Bloomberg, citing sources familiar with the matter.
Shares in the social media firm leapt on the news, though Disney investors were not as thrill by the news.
Twitter's stock price instantly added 0.5 per cent, while Disney shares dipped by the same.
The two companies aren't complete strangers: Twitter founder and chief executive Jack Dorsey sits on the board of Disney.
Bloomberg has suggested Disney would be able to help Twitter grow its video-streaming media strategy.
Disney's name has been previously dropped amongst discussions of a possible buyer. Spark Capital partner Nabeel Hyatt suggested Disney would be a good home for the company in an interview with Business Insider last week, following suggestions Salesforce and Google were about to put forward bids.
Twitter's shares whooshed higher on last weeks rumours, jumping just over 20 per cent in New York.
Reuters later quoted a source, saving the company has initiated talks with "several technology companies".
Twitter has been regarded as an increasingly attractive takeover target in recent months: its share price has fallen as it struggled to engage users.
Figures in July showed revenues had come in at $602m (£464m) in its second quarter, up 20 per cent on the year before, it missed analyst expectations of $606m.
Meanwhile, it lowered third-quarter guidance to between $590m and $610m – down from the $678m analysts had expected.