The 28-year-old was sent to West Bromwich Albion on loan in January after falling down the pecking order at Anfield.
Sturridge failed to make a significant impact at The Hawthorns due to an injury that curtailed his progress, and now he is back at parent club Liverpool.
According to Anfield Edition, Sturridge is less than impressed with Klopp after he was not invited to join the squad in Kiev for the Champions League final against Real Madrid.
Naby Keita, who is not yet an official Liverpool player as he will join from RB Leipzig this summer, is believed to have been welcomed by Klopp to watch the action in Ukraine.
The report also claims that if the Reds are to be successful this Saturday, then Sturridge will not be part of the parade to be held in Merseyside on May 27.