Grant raised the issue at a meeting of senior officials from the 'big five' sports - football, cricket, tennis and the two rugby codes - who attended a summit with ministers in Whitehall for talks on tackling fixing.
The summit followed the arrest of six people, including Blackburn striker DJ Campbell, following an investigation into alleged spot-fixing in football by the National Crime Agency (NCA).
The European Parliament wants fixing to be made a specific criminal offence, rather than rely on laws dealing with fraud or cheating at gambling, and UEFA president Michel Platini is also backing that campaign.
But Grant told Press Association Sport: "My view is that the laws are there, but it's not just the law that fixes this problem - there are a lot of other things to be done.
"The legislation is already pretty robust with criminal offences for fraud, bribery, corruption and cheating at gambling."
The sports agreed to consider setting up a hotline for players from all different sports to report approaches or information - currently the sports each have their own reporting systems.
"I will look at anything to eradicate this awful practice," added Grant. "If a unified reporting mechanism is going to make it easier for people to come forward then and provide information about cheats then we should look at it."
Grant said the meeting with the sports had been "hugely constructive".
Speaking after the meeting, the Football Association's general secretary Alex Horne insisted match-fixing is not widespread but warned against complacency.
Horne said: "I think the general consensus around the room was this isn't a big issue. The intelligence that we have says this isn't a wide-scale issue at the moment but, again, we don't want to be complacent.
"It's clear that, as Britain, we are very proud of our sporting product, of the sport that we play in this country and we all want to do all we can to protect the integrity of that sport.
"We are never complacent on this issue and there's a lot we can learn from other sports.
"Some of the education programmes that cricket have put in place are very far advanced, and the integrity unit that the British Horseracing Authority have in place is very far advanced so there's lots of learnings that are open to all sports."
The FA has its own integrity unit and education programmes, but fixing has been an issue for a longer time for horse-racing and cricket.