Chief Executive Mark Tagg confirmed that the club is seeking a replacement for Chris Rogers and is in talks with Ganguly and his agent.
''Ganguly is our first choice replacement, a player of his stature and experience would be a great asset to the club particularly during the Twenty20 Cup. We are hoping a final decision will be made next week,'' he said in a statement.
Rogers will be away from the 26th June to the 29th July, missing the whole of the Twenty20 Cup.
Earlier, Mr Tagg told BBC Sports that negotiation was on with India's most successful captain and Ganguly is likely to join the club on a five-week contract in June.
''During the Twenty20 is where we're going to miss Chris and Ganguly's a quality batsman with huge experience,'' he said.
Out of favour with the selectors Ganguly, meanwhile, will know his future when the India names the Test squad on May 24 for the away series against the West Indies.
If Ganguly joins the club, Northamptonshire will be hoping for a deadly Twenty20 partnership at Wantage Road with South African Lance Klusener also in the ranks. Coached by former Proteas skipper Kepler Wessels, the team also includes British Sikh Monty Panesar.
Ganguly last played Test cricket in Pakistan in February and was ignored for the home series against England.
Last year, Ganguly had a brief county stint with Glamorgan and the southpaw had also shared the Lancashire dressing room with England's stand-in captain Andrew Flintoff.
And if he signs for Northamptonshire, Ganguly will join Bishan Singh Bedi, Kapil Dev and Anil Kumble -- all of who have played for the county.