Now he has thrown in some intrigue off it too – posting a puzzling picture of himself with a mystery woman in a strange setting, accompanied by a strange message.
The back-in-form Liverpool striker made up for missing out on an England recall by posing in a glamorous shot with a raven-haired beauty, both of them all in black.
Standing at the front of a zebra-striped, optical-illusion style tunnel, Sturridge added to the riddle by posting the words: "Drip drip."
Some might think it should refer to his eyes – after his latest snub from Three Lions boss Gareth Southgate.
But it is more likely that some of his Instagram followers will know the true meaning.
Jurgen Klopp welcomed Daniel Sturridge's return to Anfield and, aided by injuries to others, given the striker more opportunities than he might have expectedThe 29-year-old has already netted four times this season since returning to Anfield from a goalless six games on loan with West Brom.
Indeed, Sturridge is making a serious bid to break up the thrilling threesome of Mo Salah, Sadio Mane and Roberto Firmino.
So he can afford a little fun off the pitch with his social-media snap.
Joe Gomez – one of the three Liverpool players who did earn spots in Southgate's youthful squad to take on Croatia and Spain – even rates Sturridge as world class.
The versatile defender, 21, said: "To have Studge fully fit and firing is massive for us this season. He's right up there in terms of strikers in the world.
"I could see it from the first day of pre-season. He was right on it from the get-go. He has attacked everything. He's been so focused the whole time in training."
So it is defenders as well as Sturridge's Instagram followers gazing too long at his hypnotically-framed photo, who are feeling dizzy.
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