The Reds are on their longest scoreless drought in the Premier League since March 2005, failing to find the net in three matches since a 1-1 draw with West Bromwich Albion on December 27.
Salah has gone four top-flight outings without a goal, meanwhile, firing his most recent blank in Sunday's stalemate with Manchester United.
Owen, who scored 118 league goals for Liverpool, believes that the Egypt international is no longer putting the team first.
"There is a lot of selfishness creeping in, I've seen that again," he told Premier League Productions.
"Mo Salah is not passing enough of the ball again. He's never passed it much, but there are extremes. The last sort of few games I'm thinking: 'Come on!'.