Sturridge has been without a club since March after leaving Turkish outfit Trabzonspor, who he joined after leaving the Reds on a free transfer last summer.
The 31-year-old subsequently served a four-month worldwide ban for breaching betting rules regarding a loan move from Liverpool in January 2019.
The Liverpool Echo reports he has been training with nearby Kidsgrove Athletiic - who play in the Norther Premier League Division One South East, the eighth-tier of the football pyramid in England - as he builds up his fitness with a number of Premier League and Championship clubs having been linked with offering him a deal.
“Yes, he's signed a 12-month contract," joked Kidsgrove chairman Mick Fitzjohn.
“No, he's coming down to keep himself fit and he's working hard while he finds a new club."