Speaking to City AM, Alexander said the number of ads for gambling brands during live sports broadcasts was "out of hand", and said they should be banned before the 9pm watershed.
He said it was the responsibility of the industry to be proactive: "Most people in the gambling industry think there are far too many ads. We should make the changes collaboratively with the rest of the industry, which might be difficult, and ultimately it’s up to the government to decide if it wants to legislate or not."
The call puts Alexander at odds with his counterpart at Sky Betting and Gaming, Richard Flint, who wrote in the Telegraph last month that new advertising restrictions were not the answer to tackling the problems caused by gambling.
Stephen Woodford, chief executive of the Advertising Association, told Campaign that Flint’s arguments were "spot on".
Labour has said that if it gets into power it will ban gambling advertising during live sport, with deputy leader Tom Watson an enthusiastic advocate for new regulations. Last year, Watson also said the party would ban football clubs from signing shirt sponsorship deals with gambling brands – a move that would affect nine of the 20 Premier League clubs this season.
GVC acquired Ladbrokes Coral in March.