The Argie, 65, was among the candidates for the Nou Camp hotseat before Ronald Koeman was appointed last week.
Leeds execs, fearing they might lose their manager to the Catalan giants, turned to Howe as a contingency.
Bielsa guided the fallen Yorkshire giants to this season's Championship title and a return to the top flight for the first time in 16 years.
He is now set to sign a new contract to extend his stay at Elland Road.
Leeds are not the only club to have shown an interest in Howe, 42, since he left the Cherries after their relegation from the Premier League.