NHS Ayrshire and Arran advertised the £338,500 contract in Millport for the fourth time in less than 12 months shortly before Christmas.
It is the highest level of interest to date, although previous recruitment drives collapsed because applicants wanted too much money.
In a statement, the health board said: "We have received seven expressions of interest for the Cumbrae practice contract. The full business cases must be submitted by January 31. At this time, we will have a more definitive understanding of firm interest."
The first advert in January last year attracted three expressions of interest but only one serious applicant whose business plan was rejected. A second recruitment attempt in August attracted four expressions of interest but only one candidate submitted a business plan, which was also thrown out. The third advert, in October, attracted no interest.
The island has relied on locums to provide medical cover since the previous GPs, Drs Jim and Elizabeth Bryson, retired in April last year after they were forced to close the practice's drug dispensary following the opening of a pharmacy on the island. A third GP they had employed also quit.
The couple warned that patient care would suffer if the practice lost its dispensary, which generated additional funds used to pay for out-of-hours care, home visits and the third GP. Critics said it had been used to top up the GPs' own incomes.
GPs are only allowed to dispense, as well as pres-cribe, drugs in communities where there is no pharmacy available. The controversy has led to calls for the rules to change for remote and rural communities.