The American touched down in the city on Thursday and was due to meet with Barca directors in the evening at the Via Veneto restaurant.
Sport says the transfers of Cesar Azpilicueta and Marcos Alonso, both wanted by Barça, both on the table.
Frenkie de Jong will also be discussed. The Dutch midfielder is wanted by Chelsea coach Thomas Tuchel.
Chelsea head to the United States for their preseason tour on Saturday and would like to have their squad as complete as possible.
Chelsea and Barça are also in competition for the signing of Sevilla defender Jules Kounde.
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