Awoniyi did not travel with the rest of the squad and is set to return to Belgium for another loan spell.
The Reds named a 29-man squad for their tour of US, where they will take part in the International Champions Cup.
Awoniyi only signed a new five-year deal with Liverpool this week.
The former U17 international had secured his US visa in time to be ready for a pre-season with the Reds, but was eventually left out by manager Jurgen Klopp.
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