Both players were regulars during the Italian's single season at Stamford Bridge but have not been guaranteed a starting spot since.
Calciomercato.com says the full-back position is the first priority for Sarri when he completes his anticipated move to Lazio.
The coach is said to see Alonso, 30, as a top target but the financial aspects of the deal have not yet been revealed.
A bid for Loftus-Cheek would initially be on a loan basis, as reported by Sky Italia's Gianluca Di Marzio.
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