Changes to the bill are expected to pass with bipartisan support after talks between Prime Minister Anthony Albanese and Opposition Leader Angus Taylor on Monday.
"I'm confident that later in the week we'll have the legislation in the House of Representatives with some really practical amendments dealing with the targeting of advertising, dealing with reducing children's exposure and ... the full suite of measures in a really practical way," Mr Albanese told a caucus meeting in Canberra.
"Making sure that those issues are dealt with in a constructive way, making sure that we get the balance right between people who want to go along and have a punt on a Saturday at the races, but also that problem gambling is actually dealt with."
Betting ads would be limited to three per hour between 6am and 8.30pm under the changes.
The reforms would ban gambling ads from live sport, stadiums and player jerseys.
The government has been criticised for failing to follow through on all the recommendations from a 2023 report by late Labor MP Peta Murphy, which called for a total ban on gambling ads.
Greens communications spokeswoman Sarah Hanson-Young called on Mr Albanese and Mr Taylor to have courage.
"I know there's some nervousness in the Liberal Party. They're scared of One Nation. Man up," Senator Hanson-Young told reporters in Canberra.
"Angus Taylor needs to not be scared of Pauline, and he needs to do the right thing by Australian families who are having their lives torn apart from the gambling companies."
It follows evidence given at a Senate inquiry earlier in August, where it was alleged major gambling companies offered customers inducements such as drugs and sex workers.
The industry has rejected the claims.
Labor would need the support of either the coalition or the Greens to get the reforms through the upper house.
Deputy Opposition leader Jane Hume said changes to gambling laws needed to be meaningful and protect vulnerable people.
"We'll be working with the government in good faith, negotiating with them over the next day or two to make sure that this legislation works for everybody," she told ABC Radio.
"The most important thing, though, is that we take meaningful action on those predatory inducements ... there's a lot of support for that in the party room.
"We also (want) to make sure that the laws don't weaken the existing protections that we have around gambling advertising."
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