The 26-year-old was on the bench for Saturday’s 4-1 win at Manchester City, the first time he has featured in a match day squad for the German, but that does not mean he will get a run-out in the Europa League at home to Bordeaux on Thursday.
Klopp has stressed the need for the England international to prove he will not suffer any more injury breakdowns, having seen last season decimated by thigh and calf problems which resulted in a hip operation in May.
His latest issue was a knock to his knee in training and, while he has recovered from that, it does not mean an instant return to the starting line-up.
“Daniel is coming closer and closer so he can train now seven or eight times in a row – that is the longest period since I’ve been here – and that will help him and in the end help us,” Klopp said.
“My decision you will see [on Thursday] but it is closer and that is very good.
“The most important thing in these weeks is he can train without problems.
“We have to try to bring in a situation where he is more robust.
“If he is feeling in a good moment maybe a few minutes – or more – we will see in the game.”
Klopp may opt to use Christian Benteke against the French side, having utilised the Belgium international off the bench at the Etihad Stadium in order to implement his game-plan.
But the Reds boss has said once all his strikers are fit – Danny Ings is sidelined with a cruciate knee ligament injury – it will not be a case of throwing them all into the mix.
“We have another option in Benteke, who is in good shape and that is important for us as when I came here he was injured,” he added.
“It is normal we talk about this today but it is not about bringing as many strikers as you can on the pitch – we have to work together and for this it is important you have some options.”
While there was positive news on Sturridge, that does not mean Klopp’s injury problems are easing.
“We are in a good position at this moment but in football you solve one problem and the next second you have another one,” he said.
“Martin Skrtel is a little bit ill and Mama [Sakho] is not ready for [Thursday] so we have two [centre-backs] or [have to create] a new idea.”
Dejan Lovren will be one of the centre-backs to start, having regained his place following Sakho’s knee injury.
But Liverpool playmaker Philippe Coutinho is out of the visit of Bordeaux with a hamstring problem.
The Brazil international has not yet been ruled out of Sunday’s Premier League visit of Swansea, but will definitely not feature against the French.
Bordeaux coach Willy Sagnol knows his side are not the favourites either in the match or to progress from Group B but he remains upbeat.
“This is a special moment for the club and for many reasons,” he said at his pre-match press conference.
“First of course because we have a small chance to qualify.
“We cannot compete in a full season with a team like Liverpool but in a match, with the mindset that we have displayed in recent matches, we can succeed.”
Bordeaux lie 13th in the Ligue 1 table with 18 points from 14 games.