Leonard Steinberg, chairman of the Liverpool-based group, said it could offer much better odds than winning the Lottery itself. A punter guessing three of the winning numbers could hope to get 500-1, falling to 45- 1 for two numbers and as low as 6-1 for one number if Stanley was able to offer bets on the outcome.
That compares with the 14 million to one chance of winning the Lottery.
Mr Steinberg said Stanley was already offering bets in Ireland on the Irish national lottery with considerable success.
The company echoed a warning in May by William Hill, the second-biggest chain, that the National Lottery's scratch cards were hitting sales. But Mr Steinberg admitted that the worst might be over.
"All we can say - and we don't say this with any certainty - is that interest in scratch cards is waning. That is the experience of other countries."
The picture is mixed in the rest of the industry. Coral, the number-three chain, said it felt there was now some slackening in the momentum of scratch card sales. But William Hill said the pressure had got worse since the introduction of the cards and there was no reason to imagine it had peaked yet.
A spokesman said William Hill had been demanding to be allowed to offer bets on the National Lottery since the idea was first mooted.
But he added: "We are well aware that we haven't got a hope of getting this because it would expose the very bad odds people are getting."
The comments came as Stanley announced pre-tax profits raised from pounds 12.4m to pounds 17m in the year to April. The dividend goes up 18 per cent to 6.15p.
Investment column, page 20