Speaking after the Premier League side's pre-season defeat to Porto on Sunday, Silva said the French left-back is a key target, along with Watford forward Richarlison.
Per Sport, he explained: "The English transfer market appears to be easy but it isn't. Some players have been identified but others must arrive sooner. Richarlison and Digne? We're interested in them and hope they can reinforce our squad. We'll see what happens in the next few days."
Sport added there is currently a discrepancy between the €16 million (£14 million) fee Barca want for the 25-year-old and the €10 million (£9 million) Everton are prepared to pay.
Digne has been at Barca for two years and still has three years remaining on his contract.
But he is behind Jordi Alba in the pecking order and unlikely to usurp him in the near future. He has made only 22 starts in La Liga for the Blaugrana since joining but boasts a number of very useful attributes, per WhoScored.com:
At Everton he could earn a more regular first-team spot, not least as Leighton Baines is 34 in December.
Before he moved to Barcelona, Digne played in France for Lille and Paris Saint-Germain, and has has also spent a season on loan at Roma.
He has plenty of experience playing at big clubs and could well become a major asset at Goodison Park, especially given he could still improve under Silva.