HHCL is attempting to accelerate its international strategy, put in place last year by the agency's chief executive, Robin Azis, following the loss of its Guinness and Amazon accounts to international networks.
Speaking at Chime's annual results meeting this week, Bell said HHCL would be repositioned to take advantage of international opportunities.
It is thought Bell would strike a deal involving Chime, rather than sell off the whole advertising group, which also includes the new-business development offshoot Heresy and the digital arm Digital Experiences.
It is unclear whether WPP, which has a 20.4 per cent stake in Chime, is involved in the discussions.
Since July 2001, Azis has worked at developing partnerships with overseas agencies with a new-business director working from France. Since then, the agency has won an international brief to relaunch Captain Birds Eye and a brief to launch the Russian Standard brand in Russia.
A source close to the talks said a deal would be in place by the autumn.
"It will enable HHCL to have a bigger future, and move it from the relatively small UK advertising market to an international stage. The initial efforts have not moved fast enough."