The Reds striker has endured a frustrating season at Anfield, with his playing time restricted by injury and his performances overshadowed by in-form Divock Origi.
And it seems he has yet to fully win over manager Klopp.
Sturridge was dropped from last week’s crucial Europa League semi-final against Villarreal, being forced to watch from the bench as Liverpool lost the first-leg 1-0 in Spain, when even Christian Benteke got a game.
He came straight back into the side for Sunday’s Premier League clash against Swansea, but drew a blank and the 3-1 defeat, and was then criticised for trudging off the pitch without joining his team-mates in thanking the travelling fans.
Yet, he has still made an impact for Reds – taking his tally to 51 goals in 89 games with recent strikes against Everton and Newcastle – and Murphy insists he remains one of Liverpool’s best attacking assets.
Speaking on the Alan Brazil Sports Breakfast, the former Reds midfielder said: “The simple fact is that I don’t think Daniel Sturridge is Jurgen Klopp’s cup of tea.
“In terms of ability and goal scoring prowess, Sturridge is as good as Liverpool have got and he’s one of most talented strikers we’ve got in this country.
“The problem is that when he’s not in the side and it’s not going well for him, his body language isn’t brilliant and he can maybe look as if he’s not that bothered.
“His goals-to-games ratio for Liverpool is phenomenal and as a striker, what do you do? You score goals!
“Goals win games and Sturridge is the best striker Liverpool have got. I personally want to see him playing for the club.
“But I think away from home Jurgen likes a certain type of player. Players who can do the running, the pressing and can sing from his hymn sheet. But are you telling me Sergio Aguero is brilliant at pressing?
“The bottom line is, can Liverpool sell Daniel Sturridge and use that money to get someone better? I don’t think they can.
“Sturridge knows he’s a good player and he plays with a confidence – call at arrogance, call it whatever you want – that I like to see in a player.”
Listen to Danny Murphy’s full verdict on Daniel Sturridge above!