Sefton is believed to be eager to attract a casino operator to Southport, as part of £4m plans to transform the town centre, although it insists there is no specific proposal.
Both large and small casinos will be allowed to invite a major bookmaker to set up inside, an extra attraction outlawed in existing casinos.
The larger facilities can also run bingo games. However, the maximum jackpot offered by the slot machines will remain the same, at £4,000.
During a Commons debate, Dr Pugh - asked about his "U-turn" - said he had met worried retailers and hoteliers on a visit to Blackpool, another contender for a casino.
He said: "One does not agree with absolutely every word of every report with which one is associated. I am unconvinced."
It is likely only one of Sefton, Warrington and St Helens will succeed, because the Government is insisting on a "good geographical spread" of casinos..
If the three authorities wish to stay in the casino race, they must turn their expressions of interest into firm applications before the deadline of March 31.
Liverpool - once tipped to be home a much bigger "super-casino" at Kings Dock - has now opted out of the race altogether.