Adams, who represented West Indies as player and captain during his career, replaces Englishman Richard Pybus who did not seek to renew his contract.
He is now understood to have accepted the job but is currently negotiating some details with the WICB and has not yet signed a contract.
Adams would appear to have a better chance than most of uniting all parties involved in Caribbean cricket.
He is admired for his record as a player - he averaged 41.26 from his 54-Test career - and his work as a players' representative while serving as secretary of the West Indies Players Association and president of the Federation of International Cricketers' Associations.
Pybus is expected to remain for a while to ease Adams into the position.
His first assignment will be to lead the regional team in February when England visits the Caribbean for a series of three one day internationals.