The 24-year old made it three in three Premier League outings when he netted early in his side's 1-0 home win over Manchester United and did it with a slight thigh injury in front of England boss Roy Hodgson.
The Three Lions take on Moldova and Ukraine in World Cup qualifiers on Friday and Tuesday respectively but Sturridge expects to be fit to hopefully carry on his scoring form at international level.
"It was great to have the manager here, it's important for me to be out on the field," Sturridge, who has scored five in four in all competitions this term, told Sky Sports 1.
"I had a problem with my thigh before the game, it's still hindering me now, but I went out and put on a good performance for the boys.
"Hopefully I'll be okay for the (England) squad."