The inaugural season of the much-awaited tournament will feature eight teams and is scheduled to start on July 21.
This move would open opportunities for players who do not get an IPL contract.
Bairstow was allocated to Welsh Fire last year. However, the 31-year-old wicketkeeper has missed out on a central Test contract and thus the side needed a replacement.
The inaugural season of The Hundred, scheduled for July, was postponed due to the coronavirus pandemic.
ECB's comments have come after UK Prime Minister Boris Johnson said the lockdown won't be ease anytime soon considering the transmission rate of the deadly coronavirus.
The idea of private investments wasn't in the agenda when the event was being conceptualised but the financial turmoil has forced ECB to reconsider its stance.
The men's squad for the competition was chosen based on the draft in October 2019, while the process of filling the women's squads was pending completion.
The big-hitting opener is disappointed not to be able to build on the goodwill earned from that thrilling World Cup success on home soil.
Graves is expected to take over as ICC's next chairman, replacing Shashank Manohar.
The inaugural season of The Hundred has been postponed until 2021 following an ECB board meeting held on Thursday.