Source: Sharecast
Under current rules, savers can pay £20,000 annually into an ISA without incurring tax.
But according to the Financial Times, Reeves is considering halving the cap to £10,000, in the expectation people will shift funds out of cash ISAs and into domestic stocks.
An unnamed ally of Reeves told the newspaper: "She wants to see people investing more in British stocks because it’s good for growth and it generates better returns for savers.
"But we can’t win the argument on our own. Lots of businesses support the idea but never say it."
Reeves first mooted the shake-up earlier this year, but her plans were halted after widespread opposition from banks, building societies and consumer groups.
In particular, building societies argued that money deposited into ISAs was vital to fund mortgages and home purchases.
Investing in stocks rather than saving accounts such as ISAs is also more risky.
ISAs have proved immensely popular since they were introduced in 1999 by then-chancellor Gordon Brown. More than 18m people now have one, with an estimated £300bn sitting in their accounts.
Neil Wilson, UK investor strategist at Saxo Markets, said: "It will take a lot more than tweaking around with allowances for retail investors [to invest in UK equities]. And I’m not sure about the second order effects - do you move up the risk curve or just plump for a less tax efficient cash rates?
"This has been discussed a lot already but suffice to say a stick is maybe not as good as a carrot."
Reeves is due to present her Budget to Parliament at the end of November.
While keen to bolster sluggish economic growth, she is also facing a number of headwinds, including soaring government spending, sticky inflation and higher borrowing costs.
Tax rises are increasingly seen as inevitable, despite manifesto pledges to the contrary.
The private sector is also lobbying hard to prevent any further cost hikes for businesses, after increases to both the minimum wage and employer’s National Insurance contributions came into effect in April.
