The government said in October it would reduce the top stake on the machines from 100 pounds to between 50 pounds and two pounds, with the limit agreed after a consultation that ends on Tuesday.
Fixed odds betting terminals (FOTB), which allow players to bet on the outcome of various games, are an important source of income for high-street bookmakers.
Britain's bigger bookmaker Ladbrokes Coral made about 800 million pounds of revenue from gaming machines in 2016.
The terminals have been called the "crack cocaine of high street gambling" by critics as they allow players to bet as much as 300 pounds a minute on high-speed games such as roulette.
A report by industry regulator the Gambling Commission last year said 43 percent of players were either problem gamblers or at risk of becoming a problem gambler.
Bookmakers, however, say they would be forced to close high-street stores if they lose the income form the machines. William Hill said in October it was concerned that "severe" cuts in the maximum stake were an option in the review.
The Sunday Times said the "overwhelming" response to the review had persuaded the government to reduce the maximum to two pounds.
"Matt (Hancock) wants the new stake to be at the bottom of the range," the newspaper quoted a Hancock ally as saying.
"His attitude to (the terminals) is very negative because it takes money from reasonable, mature betting, like on the horses."
A Department for Digital, Culture, Media and Sport spokeswoman said the government was "currently consulting on what the exact cut should be, and would make a final decision in due course once all the evidence has been considered".
"We are clear that FOBT stakes will be cut to ensure we have a safe and sustainable industry where vulnerable people and children are protected," she said.
($1 = 0.7217 pounds)
(Reporting by Paul Sandle; Editing by Adrian Croft)
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