Olympic ticketing is a multi-million dollar business while it was responsible for around 30 per cent of the revenue raised by London 2012.
But it is an issue that has also caused huge controversy, particularly at London 2012 when thousands of sports fans were left disappointed at not being able to secure tickets for the Games.
"I am of the opinion that the IOC should go into the ticketing business and handle the ticketing for the Olympics," Sir Craig said here today.
"The IOC should be responsible for distributing Olympic tickets worldwide and they should help the Organising Committee in distributing tickets in the host nation.
"It would be a huge help to the Organising Committee with the expertise the IOC could provide.
"With some host cities, raising revenue from tickets is not always a big thing but with other cities, like London, it was a huge part of the commercial operation to raise revenue.
"But whoever the host city is, I think there would be a much smoother situation if the IOC was running it."
Sir Craig's comments come following a major ticketing scandal within the Olympic Movement earlier this year when a Sunday Times investigation alleged that people around the world had been caught offering to sell thousands of tickets on the black market, including for the top events like the men's 100 metres final.
The general secretary of National Olympic Committee of Ukraine, Volodymyr Gerashchenk, was also forced to resigned after the BBC filmed him offering to sell thousands of London 2012 tickets on the black market.
The scandals came when a total of 1.2 million Olympic tickets were released to National Olympic Committees (NOCs) around the world for London 2012, who bid for their share of the ticket allocation based on demand in their countries.
This system resulted in officials exaggerating local demand so they could get the maximum number of tickets despite them being forbidden to sell their tickets abroad or to anyone who plans to resell them.
The IOC could claim that they would prevent a recurrence of this but any move to take control of the hugely lucrative business could be met with huge opposition, particularly from host cities who could stand to lose billions to the IOC if ticket distribution was centralised by the Olympic governing body.
Contact the writer of this story at firstname.lastname@example.org
June 2012: London 2012 ticket story is untrue and "misleading", claims head of Hellenic Olympic Committee
June 2012: Ban them from Olympic Movement, says Oswald after London 2012 ticket allegations
June 2012: Emergency IOC Executive Board meeting held after London 2012 ticket scandal
May 2012: Ukrainian NOC general secretary resigns over London 2012 ticket scandal
May 2012: Ukrainian Olympic Committee secretary general suspended after London 2012 ticket scandal