Sturridge shone in Wednesday's 3-0 friendly win over Sydney FC in Australia, but it has emerged that he was playing through the pain barrier for the opening 45 minutes after completing a gruelling 24 hours of travelling.
Asked if he wanted Sturridge to stay put, manager Jurgen Klopp said: “That's not the question, it's nothing for here.
“Whatever I say it would be a headline and I don't want headlines after the season. I am fine with the headlines already."
“What can I say? This kind of football game makes it easy to enjoy what they are doing.
“We speak about everything. We spoke, we speak. It's not just a case of starting with things now.
“It's not just my talks, it's talks with (sporting director) Michael Edwards, with agents or whatever. We speak to everybody. In the end, everybody will know what happens when it happens.
“It is not always in our hands. It's not just about Daniel. That's how transfers work - whether someone stays or not. There are a few things still to do this summer but we have time.
“We will look who we bring in and then we will see who wants to leave. At the end of August at the latest, then we will have a squad. It's not very likely it will be all done on July 5."