Luongo's future at Championship club Queens Park Rangers remains shrouded in doubt after manager Mark Warburton confirmed the 26-year-old's desire to move on from the Kiyan Prince Foundation Stadium.
And though Leeds looked the likeliest destination for the former QPR captain, who has been left out of their pre-season program, that no longer appears to be the case.
According to the London Football News, Leeds hierarchy have baulked at QPR's asking price for the Australian, believed to be in the region of £4 million (A$7.2 million), and now view Stoke City's Ryan Woods as the next best target.
With Woods' transfer fee likely lower than that of Luongo's, any potential deal would leave less of a mark on the club, who recently announced a £4 million loss under owner Andrea Radrizzani.
Bielsa's decision to pursue another option in central midfield is also dependent on the future of Kalvin Phillips.
The Whites star has been linked with a £30 million (A$54 million) move to newly promoted Premier League side Aston Villa, though no formal offer has yet been submitted.
Regardless of Leeds' decision, Luongo will likely find himself playing in new colours next season as QPR look to land a deal before his current contract comes to a close in June 2020.