Sturridge, 28, went to West Brom on loan in January but was injured early on and managed just six appearances.
With 12 months left on his contract it appeared Sturridge's Anfield career was over but he has looked sharp in his five friendly games and Klopp, who became frustrated by the player's unavailability last season, is prepared to hand him a lifeline.
"We're not in doubt -- and nobody was ever in doubt -- about his quality," the Liverpool manager told liverpoolfc.com.
"In this moment he looks really good to be honest. That's cool -- really cool for him and cool for us. (It's) a very important moment for him. I am in talks with him, what he feels.
"I don't want to make him the most physically strong player in the squad or whatever.
"The most physically strong player in the squad cannot play football like Daniel Sturridge and he has no possibility to be that, to be the marathon man of the team, but he can be a very decisive player."
Sturridge could be in line to start the Premier League campaign at home to West Ham on August 12, with Roberto Firmino and new goalkeeper and fellow Brazil international Alisson only rejoining the squad at next week's training camp in France.
Liverpool are currently taking part in the International Champions Cup in the United States.