And if the Blues complete the signing of the 24-year-old, Sarri could risk the wrath of his squad by dropping Azpilicueta.
Chelsea have already signed Christian Pulisic this month although he has been sent back to Borussia Dortmund for the rest of the season.
And the Blues are hoping to complete a deal for Gonzalo Higuain before midday on Wednesday.
That would mean he could play against Tottenham in the second leg of their Carabao Cup semi-final on Thursday.
Cesar Azpilicueta could be replaced by one of Maurizio Sarri's trusted pupils (Image: Getty)
Maurizio Sarri has placed trust in Cesar Azpilicueta this season but could be willing to axe him (Image: Getty)
Sarri is eyeing Hysaj with Victor Moses and Davide Zappacosta set to leave Stamford Bridge this month.
Higuain enjoyed the most successful spell of his career under the Chelsea boss and will hope to replicate that form should the move be completed.
But questions remain on the future of Eden Hazard after he spoke again about potentially joining Real Madrid in the summer.
“I have won everything in England, apart from the Community Shield, but that doesn’t mean that I’m leaving,” he said.
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