Ghana Football Association president Kwesi Nyantakyi said Grant was the preferred candidate of five whose applications were considered.
Grant and Spanish coach Juan Ignacio Martinez were interviewed, Nyantakyi said, adding: “But our preference is Avram Grant on the details of the job requirements and expectations.”
If he accepts the terms, Grant could be in charge in time for Ghana’s final Africa Cup of Nations’ qualifiers away to Uganda on November 15 and at home to Togo on November 19.
Grant held a string of management positions in his native Israel, including four years as coach of the national side.
He moved to English outfit Portsmouth as technical director in 2006 and then to Chelsea as director of football, taking over from Jose Mourinho when he was sacked in September 2007.
But his time at Stamford Bridge was short-lived and his contract was terminated at the end of the season, despite guiding the Blues to the runners-up spot in the Champions League and Premier League.
Following a return to Portsmouth, he quit and joined West Ham in 2010 but was sacked after the Hammers were relegated.
He went on to manage Serbian side Partizan Belgrade and will come to Ghana from Thai club BEC Tero Sasana in Bangkok, where he is currently technical director.
Ghana have been without a coach since September 12, when Appiah was sacked following a turbulent World Cup finals in which Ghana failed to advance beyond the group stages.
Before the team’s decisive group match against Portugal, which could have seen them reach the knock-out stage, players demanded that over $3 million in appearances fees be flown to them in cash.
The demand caused an uproar in Ghana, where a slowing economy and a devaluing currency have sent prices rising across the country over the past year.
The GFA then suspended striker Kevin-Prince Boateng for insulting Appiah and midfielder Sulley Muntari for hitting a staff member.