According to the BBC, a deal has been struck between the two leading candidates for the job, Morgan and Sharad Pawar, the president of the BCCI, who met in private this week in a bid to overcome the impasse that was created after an ICC governance committee cast equal votes for the two candidates earlier this year.
There had been some speculation that the job could have been decided on the toss of a coin, but instead both candidates will become vice-presidents, in effect presidents elect. Morgan will take the helm next year for a two-year tenure, with Pawar succeeding him in 2010 - in time to take control of the 2011 World Cup in the Subcontinent.
The ICC executive committee is currently in London for a series of meetings ahead of the annual conference at Lord's on Friday. Mali will take the chair left vacant by the untimely death in May of his predecessor, Percy Sonn, but the news of an agreement between Morgan and Pawar is a welcome development at the end of an unsettled period for the organisation.
A formal announcement of the agreement is expected later in the week, as the ICC embarks on a tricky agenda that will include the fall-out from the recent World Cup, and the ongoing situation in Zimbabwe.
Morgan, 69, has been the chairman of the ECB since January 2003, and prior to that was at the helm of Glamorgan County Cricket Club. He was seen as a "safe pair of hands" when elected to succeed Lord MacLaurin, but attracted criticism for his handling of the Zimbabwe question in particular.