The striker has been sidelined by a thigh complaint that forced him to withdraw from the England squad that will face Brazil this evening.
However, having received treatment, Marsh is hopeful that Sturridge, as well as Raheem Sterling, will be available for the visit of the Baggies to Anfield.
"They've both been in for treatment. They were not available to play for England due to the injuries they've picked up," Marsh told the club's official website.
"Raheem's has been a bit more long standing. In old-school terms, he's got a dead leg and Daniel picked his up at the weekend. With a bit of luck and treatment hopefully they'll both be available for Monday night."
The Reds will go into the contest seventh in the table.