Former India captain Gavaskar, following a series of contentious comments, met with ICC chief executive Malcolm Speed at the global governing body's headquarters in Dubai on Wednesday.
An ICC statement said "Sunil will convey his views to the ICC " having chaired the upcoming meeting of the ICC Cricket Committee on May 5-6.
"The ICC board will then review the issue at its annual conference between June 29-July 4.
In January, Gavaskar criticised match referee Mike Procter for the way in which the former South Africa all-rounder found Harbhajan Singh, the India off-spinner, guilty of racially abusing Australia's Andrew Symonds, a decision overturned on appeal.
"By accepting the word of the Australian players and not the Indian players, the match referee has exposed himself to the charge of taking a decision based not on facts, but on emotion," Gavaskar wrote in the Hindustan Times.
"Millions of Indians want to know if it was a 'white man' taking the 'white man's' word against that of the 'brown man'."
Gavaskar's remarks did little to defuse an already volatile situation and led to questions over whether it was right for someone in his position to make such public comments about a fellow ICC official.
Then, after the ICC's executive board meeting in Dubai last week, Gavaskar turned his attention to the boards of England and Australia, who he said needed to recognise India's increasingly influential role in world cricket.
"Gone are the days when two countries, England and Australia, had the veto power in international cricket, even though the dinosaurs may not open their eyes and see the reality," he wrote.
"The cricketing world has found that India has no longer a diffident voice but a confident one that knows what is good for its cricket, and will strive to get it."