The Whites filled their priority positions earlier in the transfer window by landing defender Robin Koch and forward Rodrigo, but they are still looking for reinforcements.
Leeds are interested in Udinese midfielder Rodrigo de Paul, but have so far been unwilling to meet the Italian club’s asking price for the Argentine.
Now they are showing interest in another Serie A performer in the shape of Pulgar, who is on the books at Fiorentina.
Leeds are ready to pay €15m to take the Chile international to Elland Road, according to Italian daily La Nazione.
Such a sum could be tempting for Fiorentina, who snapped up Pulgar from fellow Italian side Fiorentina last summer.
He caught the eye with his performances in a purple shirt over the course of last season and Fiorentina could sell him to then reinvest the cash in the transfer market.
Pulgar, 26, has won 24 caps at international level for Chile; Leeds boss Marcelo Bielsa had a spell as Chile coach from 2007 until 2011.