The incumbent is St Luke’s, which picked up the business in October 2005.
Heineken has approached shops on its creative roster, including St Luke’s, to pitch for the account.
St Luke’s, which celebrated its 20th anniversary last year, created a campaign in 2014 showing the hard work that farmers put into growing apples for Strongbow. The brand’s advertising had pre-viously centred on people "earning" a pint of the cider.
As well as the Heineken beer brand, the brewer also owns Bulmers, Foster’s and Kronenbourg 1664. Adam & Eve/DDB and Ogilvy & Mather both work with the company in the UK.
A Heineken spokeswoman said: "St Luke’s has provided us with excellent creative campaigns over a number of years.
"We are now in discussion with our three agencies, including St Luke’s, about who will be best to take on the next chapter in the Strongbow story. This is a closed process and we have not invited other agencies to participate."
Heineken added 101 to its global roster without a pitch earlier this month. The agency will handle strategy and creative activity.
Starcom Mediavest Group manages Heineken’s global media planning and buying. The Publicis Groupe agency won the brief in 2012.