The Black Cats are understood to have lodged a Â£3million bid late last week, an offer rejected by the Champions.
Unsettled Ulloa has started only one Premier League game this season and is keen to move in order to secure first team football.
He handed in a transfer request earlier this month, with Sunderland boss David Moyes keen to bring him to Wearside.
The Argentinian is a player long admired on Wearside and is currently fifth choice at the Foxes, behind Jamie Vardy, Islam Slimani, Shinji Okazaki and Ahmed Musa.
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A key part of their stunning title victory last year, Ulloa appeared to a confirm a departure was imminent, taking to social media on Saturday night to say, “Thanks to all the fans at LCFC. Two wonderful years but I need to feel like a footballer again.”
However, Leicester boss Claudio Ranieri has warned that the the 30-year-old will not be sold on the cheap.
“If somebody wants Leo they will have to pay. They have to pay because he is a good player and that is it."
Leicester are thought to value the former Brighton striker at Â£11million, and the Black Cats face a fight to try to drive down that price.
There have been mixed reports over how much Leicester want for the striker, with some suggesting Â£5million may be enough to land his signature.
Meanwhile, The Times are reporting Sunderland are set to sign Everton duo Bryan Oviedo and Darron Gibson with medicals scheduled for Monday at the Academy of Light.
Sunderland's interest in Oviedo comes after Patrick van Aanholt's move to Crystal Palace in a deal worth up to Â£14million.
That transfer should finally be confirmed today.
Moyes is due to hold his pre-match press conference this afternoon ahead of the Tottenham Hotspur game tomorrow night at the Stadium of Light.
The Sunderland boss meets the press from 1.30pm and we'll have the very latest news via our live blog.