South African Ford, 46, who is contracted with English county Kent as director of cricket, was on Saturday selected as coach of the Indian national team for a one-year period.
India's cricket chiefs have given Ford until Monday to tell them when he can take up his new job. They hope he will be in place ahead of the tours of Ireland and England starting later this month.
But Kent, where Ford is contracted until September 2008, said they would not discuss the coach's future until Sunday's one-day match against Hampshire in Tunbridge Wells was over.
A statement by Kent's chief executive Paul Millman, posted on the county's official website, also wished "the popular South African" would continue with them.
"The focus for Graham and the Kent team is very much on winning a match that would see the team edge a step closer to a home semi-final in the Friends Provident Trophy," the statement said.
"Discussions with Ford will take place after the match and ... it is hoped that the popular South African will remain at Canterbury to continue the progress made towards re-establishing Kent as a major force in county cricket."
Another Kent online website reported the county "seem certain to demand some form of compensation package from the Indian board for losing their man."
An Indian cricket board panel picked Ford over Englishman John Emburey, the only other candidate for one of the most high-profile jobs in cricket, after closed-door interviews in Chennai on Saturday.
"The panel has decided to appoint Ford initially for a period of one year," the board's treasurer, N. Srinivasan, told reporters after the meeting.
Ford was chosen to succeed former Australian captain Greg Chappell, who quit after India crashed out in the first round of the recent World Cup in the Caribbean.
Media reports said Ford, who was South Africa's coach from 1999-2001 when the Proteas won nine of their 11 Test series, was recommended by India's captain Rahul Dravid, a former Kent player.
Dravid had also persuaded the board to sign up another Kent coach, New Zealander John Wright, in 2000.
Wright served as India's first foreign coach until 2005 when he was succeeded by Chappell for a two-year term.
Ford's first major assignment with the Indian team will be three one-day internationals against his native South Africa in Belfast, Northern Ireland, in June ahead of a full Test tour of England from July.
Ford played first-class cricket and football for Natal and was a qualified rugby union referee before he made a mark in cricket coaching.
The panel that selected him was headed by Indian board president Sharad Pawar and included three former captains -- Sunil Gavaskar, Srinivas Venkataraghavan and Ravi Shastri.
Coaching jobs are still up for grabs in the three remaining Asian Test nations.
Pakistan coach Bob Woolmer died during the World Cup, while Sri Lanka's Tom Moody and Bangladesh's Dav Whatmore quit soon after the showpiece event.