Sturridge and Milner look set to miss the start of the campaign.
Liverpool may have been handed a blow on the eve of the new Premier League season, as striker Daniel Sturridge is a doubt for the opening fixture against Arsenal next weekend, according to the Daily Express.
Sturridge struggled with injury problems yet again last season, managing just 25 appearances in all competitions, although he still posted a respectable goal return with 13 strikes in those games.
The 26-year-old has only managed more than 14 Premier League matches in one of his three full seasons at Anfield, and has played just 26 times in the league since May 2014.
He appeared to have hit full fitness over the last few months since returning to action in February, and ended last term with six goals in his final nine games, as well as scoring an injury-time winner after coming on as a substitute for England against Wales at Euro 2016.
Although Sturridge's latest problem is though to be a minor recurrence of a hip injury rather than a major new problem, he missed Saturday's 4-0 win over Barcelona and will also be out of the game against Jurgen Klopp's former side Mainz on Sunday.
That is likely to effectively end his hopes of starting against Arsenal when the Reds take on the Gunners next Sunday.
Meanwhile, Reds boss Klopp admitted after the 4-0 friendly demolition of La Liga giants Barcelona on Saturday that midfielder James Milner has suffered an injury which looks ominous.
Milner was forced off before half-time in the victory and Klopp told the club's official website: "Milly, it doesn’t look too good. We have no real idea what it is but it’s something with the heel and we have to do a scan and then we’ll know more."