A person familiar with the matter told Bloomberg that the chancellor is set to announce a consultation on the plans at next week's Autumn Statement, alongside other changes to the ISA regime.
Andrew Griffith replaced as City minister by former HSBC executive
HMRC's existing policy prevents ISAs from holding fractional shares of stocks, or less than a full share of a stock, which can require investors to sell their stakes and incur taxes on the gains.
According to Bloomberg, some market participants have expressed criticism of the policy, prompting trading apps to urge clarification from Hunt on the matter.
Earlier this week, a group of fund management and financial services bosses wrote an open letter to the chancellor calling for an ISA "reform" at next week's Autumn Statement.
The group, which included signatories such as John Ions at Liontrust and Mike O'Shea, CEO of Premier Miton Investors, called on Hunt to tackle the "downward spiral of investment and lower valuations", which they said "has taken hold" in the UK.
Financial services CEOs call for ISA 'reform' at Autumn Statement
They said this has resulted in companies being taken private and looking to international markets, "stifling growth and affecting the tax revenues crucial for funding public services".
Reforming ISAs in next week's statement would "help reverse this by putting the £68bn a year invested into ISAs to work on behalf of the UK economy", they added.
The Treasury has been contacted for comment.