The council has been active in recent years in attracting other major events to McLean Park such as a rugby test between the All Blacks and Argentina and an Australian NRL rugby league match between Melbourne Storm and St George Illawarra Dragons, both in 2015.
But he said the sevens tournament "seems to have done its dash" and was not as popular as it had been in earlier years.
Hawke's Bay Rugby Union chief executive Mike Bishop said the New Zealand union had asked for expressions of interest.
These would include Wellington deciding whether it wished to continue holding the tournament, which this year was held on the last weekend of January but which had previously been held on a week late, sometimes coinciding with Waitangi Day.
If it were to be seriously considered for Hawke's Bay, the union would work with the city council, but he said a lot of issues needed to be considered, including availability of accommodation for teams from at least 16 countries and visitors.
According to reports, Auckland, Hamilton, Dunedin and Christchurch are being touted as possible hosts as the IRB and New Zealand Rugby Union move to revitalise the tournament, although the New Zealand Rugby Union has asked all provincial unions for expressions of interest.