Simone Zaza (right) is currently at Euro 2016 with Italy
The Foxes could lose Jamie Vardy in a £20million move to Arsenal this summer and are drawing up contingency plans for the departure.
Leicester are said to be eyeing swoops for Watford's Troy Deeney and Ahmed Musa of CSKA Moscow.
Chelsea, meanwhile, are reportedly in the market for two strikers, with Diego Costa's future unclear as Atletico Madrid seek to re-sign their former frontman.
And Italian newspaper Gazzetta dello Sport claim both clubs are keen on landing Zaza, who is valued at £23m.
Morata could join Real Madrid this summer but even if he does there appears little chance of Zaza earning game time in Turin.
Juve want to sign Paris Saint-Germain's Edinson Cavani to replace Morata, while they are also reportedly keen on Sassuolo's Domenico Berardi and Romelu Lukaku of Everton.
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Vardy's club at the end of the summer transfer window: