Poveda, who is out on loan at Championship club Blackburn, faces a lengthy spell on the sidelines after breaking his fibula and suffering damage to some ligaments.
The winger had to be stretched off before the second half in a 1-1 draw against Bristol City last weekend and could be sidelined until the end of the season.
Bielsa has revealed that Leeds have been in touch with Poveda to express their sadness about the injury.
“We have established contact with him, all of the technical staff to know about our sadness and we will be close after what has happened with him”, Bielsa said at a press conference.
However, the veteran Argentine manager feels that the young winger has a lot of character which will allow him to recover and return stronger.
“He is a young man with a lot of character.
“That is going to allow him to recover and come back stronger than before.”
Since his debut for Leeds United in June last year, Povda has featured in 20 games for the Whites, but was allowed to go out on loan at the start of the season in order to gather more first-team experience.