The Egyptian winger, who trained with the first team at the AXA Centre in Kirkby on Monday, was not included in the travelling squad announced by Liverpool.
Salah said on Saturday that he felt “thrown under the bus” by Liverpool and that his relationship with Slot has broken down, after being left on the bench for a third successive match in the 3-3 draw against Leeds Utd.
Reports suggest that his omission from the trip to Italy is a result of a selection decision rather than a disciplinary measure.
According to the BBC, the decision has the full support of Slot and is intended to allow the player a short period away from the squad following his public remarks.
It is understood that there are to be no formal disciplinary proceedings against Salah.
Liverpool host Brighton in their next Premier League fixture before Salah departs for the Africa Cup of Nations with Egypt.
The 33-year-old is Liverpool’s third-highest goalscorer of all time, with 250 goals in 420 appearances.
This season, however, has been difficult for Salah, who has scored just four times in 13 league appearances, as the reigning champions find themselves ninth in the Premier League table.