The process is in its early stages, with a formal pitch expected in October.
It is not known whether the incumbent on the business, Play, will defend the account.
The agency, part of the M&C Saatchi group, has handled digital advertising for Twinings since 2006, when it was hired to redesign its website. It subsequently launched a global site in 2007, promoting the tea brand's 300-year heritage.
The successful agency will be briefed to produce online ad campaigns that will seek to improve Twinings' market share.
The tea is the sixth-most-popular hot beverage brand in the UK, according to TNS Worldpanel figures published this month, with sales up 9 per cent year on year.
The digital review comes shortly after Twinings completed its five-month advertising review by splitting the £4 million account between the three pitching agencies.
Adam & Eve was handed the Everyday Teas account, Abbott Mead Vickers BBDO took on the advertising for its speciality teas, and WCRS won the Options and Ovaltine task.