Having had a €15 million offer thrown out by Barca, Tuttosport says Juve have upped their bid to €18 million plus €3 million in bonuses.
Juve chief Beppe Marotta chose to return to the negotiating table after positive talks with Alexis' agent, Fernando Felicevich.
Barca coach Luis Enrique is willing to sacrifice Alexis as he seeks funds for a new striker signing.
Manchester United are prepared to outbid Juve for the Chile dazzler, but Alexis favours Juve because of the English giants' lack of Champions League football.
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