The Italian champions are on the hunt for a new central midfielder now after Paul Pogba completed his move to Manchester United.
Matic is high on Juventus’ list of targets and the club are determined to tie up a deal before the transfer window closes.
Initially the Italian side had been preparing a bid of around £25m but now, according to Mediaset Premium, they are ready to use Zaza as part of the deal.
The striker wants to leave Turin this summer and Juve hope that his inclusion in any transfer for Matic will help seal the switch.
Zaza has previously expressed a desire to remain in Italy, but it is understood that he could be tempted to England by the prospect of working with Chelsea boss Antonio Conte.