Bielsa, 60, a former Argentina and Chile boss, resigned from French club Marseille in August and is unattached.
He led Spanish club Athletic Bilbao to the 2012 Europa League and Copa del Rey finals before a 2014 move to Marseille.
Swansea parted company with Garry Monk on Wednesday and are thought to want a new boss before Sunday's West Ham game.
Monk left the club following a run of just one win in 11 Premier League games.
AEK Athens boss Gus Poyet was thought to be in the frame to replace him, but the Greek club said that they had not received an approach from Swansea regarding Poyet.
Sevilla manager Unai Emery has also been linked with the job.
Swansea's first-team coach Alan Curtis was in caretaker charge of Saturday's 2-1 defeat at Manchester City.

The ancient berry is from the same family of plants as potatoes, tomatoes and peppers.
On the fossil, you can see the lines of the papery wrapping that grew around the fruit, which turned into coal during fossilisation.
It was found in the Patagonia area of Argentina and researchers are hoping to find lots more plant fossils there.
That's not the only place where old food can been found. We'd recommend you didn't eat these examples, which are all definitely way past their sell-by date!
This huge 2,000-year-old lump of butter was found in a bog near Drakerath in Ireland last year.
It probably wouldn't fit inside your fridge - it weighs as much as 10 large bags of sugar.
Conditions in bogs are good for preserving things so the butter is in a good state, even though it's so old.
It does, however, smell like strong cheese. We're not sure which would smell worse, this butter, or...
Last year, divers were exploring a shipwreck buried deep under the sea near Sweden when they found this jar.
They didn't know there was cheese inside until the journey to the surface caused some of the contents to leak, releasing a very strong smell.
The stinky discovery was made when the team were investigating the wreck of the Kronan, a warship that sank 340 years ago.
Now that's taking mature cheddar to the extreme!
In 2015, an American couple revealed they were still eating their wedding cake, 60 years after it was first baked in 1955.
Ann and Ken Fredericks, from Florida, decided to eat one piece of the fruit cake every year to celebrate the day they got married.
They said their children were horrified at them eating such old food but insist that it still tastes as good as ever!
We're wondering how long it'll take them to finish the whole cake...

Traditionally, bonfires are lit in many loyalist areas to mark the start of the annual commemoration of William of Orange's victory over King James II at the Battle of the Boyne in 1690.
The Northern Ireland Fire and Rescue Service said they had resolved 13 bonfire incidents on Tuesday night.
However, it said it was also responding to a "significant number" of other bonfire-related callouts.
The PSNI say they are investigating complaints about "distasteful" materials placed on some bonfires.
Sinn FÃ©in National Chairperson Declan Kearney called on unionist politicians to condemn "hatemongers" who put a replica coffin bearing the image of Martin McGuinness, who died in March, on a bonfire in east Belfast.
"I am directly challenging the leaders of all unionists parties to immediately disassociate themselves and their parties from this and other examples of sectarian hate crime," he said.
Martin McGuinness' son Emmett tweeted: "I am very thankful that I was raised by parent's never to hate anyone or anything. Michelle O'Neill is right, the annual display of hate must end."
Images also emerged on social media of a bonfire in east Belfast draped with a banner carrying a racist message directed at Celtic footballer Scott Sinclair.
In a statement, the PSNI said: "Police are investigating complaints about various materials, some of which are clearly distasteful, placed on the bonfire.
"Where police are aware of a crime being committed, an investigation will follow.
"We take hate crime very seriously and actively investigate all incidents reported to us," it added.
Earlier on Tuesday, a number of homes close to a large bonfire in east Belfast were boarded up to protect the properties from heat damage when the fire is lit.
Swansea City chairman Huw Jenkins is in South America as he steps up the search for a new manager, with Argentina's Marcelo Bielsa the odds-on favourite.
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A 52 million-year-old fruit fossil has been discovered in South America.
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Eleventh night bonfires have been taking place across Northern Ireland.