The 23-year-old has endured a largely unsettled career since emerging from the youth setup at Camp Nou - moving to Roma before returning to Barcelona.
He spent last season on loan at Ajax and is out of contract with the La Liga giants at the end of next term - fuelling speculation he will again leave the club permanently.
With Torino losing last season's top scorer Ciro Immobile to Borussia Dortmund, Krkic's agent Diego Tavano says there is interest in the move on both sides.
"Toro like Bojan, but Bojan also likes Torino," he is quoted as saying by Tuttosport.
"It would be the ideal club for him to get back to the top level.
"He would very much like to embark on a Granata adventure. It’d be perfect for him."
Ajax had an option to re-sign the forward on loan for a second season but opted against it, with Bojan having scored only five times in 32 appearances for the Dutch champions last term.
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