Shipping magnate Sir William Burrell, who gifted his art collection to the city in 1944, stipulated in his will that items should not be allowed to leave the country for fear of them being damaged.
But Glasgow City Council, Glasgow Life, which runs the city's museums, and the Burrell Trustees believe travel is now safe enough to render the stipulation out of date.
They want to tour pieces abroad while the building housing the collection is closed between 2016 and 2020 for a major, £40 million revamp.
But first the Scottish Parliament must agree to remove the restrictions on travel imposed in Sir William's will.
Four MSPs on the committee considering the Burrell Collection (Lending and Borrowing) Scotland Bill heard submissions from a number of experts.
They included Glasgow Life chairman Archie Graham, Glasgow Life chief executive Bridget McConnell and Sir Angus Grossart, chairman of Burrell Renaissance, the group overseeing the museum's revamp.
The MSPs have already received submissions from a number of organisations, including Museums Galleries Scotland, which is in favour of allowing the collection to leave Glasgow.
It insists national and international standards exist to ensure transportation of museum collections are conducted under strictly observed conditions.
But Dr Nicholas Penny, director of the National Gallery in London, says moving works of art has led to several incidents and damage to works which have not been reported.
He said he knew of 10 major accidents in transported art during his 27 years working in museums.
Committee chairwoman Joan McAlpine MSP said: "It is a very impressive collection but from the tour we did, it is clear there are serious problems with the building in terms of water ingress from the roof. The building is in a poor state and is endangering some of the art works."
She said Glasgow Life hopes to take the collection on an international grand tour to some of the top galleries in the world.
Ms McAlpine added: "Taking it to five or six of these galleries will enhance the reputation of the collection, of Glasgow and Scotland and increase visitor numbers.
"However, the committee have had to take an oath of impartiality so are keeping an open mind."
The committee will hear further evidence in two weeks with the Scottish Parliament likely to make a final decision in November.
Councillor Graham said: "We believe we have an opportunity to realise the full benefits of Sir William's gift.
"That would benefit the people of Glasgow through reciprocal loans, bringing some of the world's finest treasures to our city.
"I'm delighted to have been able to make our case to the committee and, I hope, that when all the evidence is presented, they will agree with us, that the time is right to unlock the potential of this outstanding collection."