Looking at the Alisson Becker's pass to Mo Salah here you can see that Salah receives it in Liverpool's own half. We don't have a clear shot of where Salah was at the time of the pass, but given his distance from midfield and the direction he's running, it's clear that he was in Liverpool's half at the time of pass.
Offside can only happen when the offensive player is in the other team's half. See this Sports SE question for more info on when a play is an offside.