The Dutch international missed the club's last two league games, along with their last game in the Europa League, having suffered a knee injury during Liverpool's 2-1 loss at Tottenham Hotspur, their only defeat this season.
"Cody is in full training now since Sunday, which means he's available for the squad," Klopp told reporters.
Andy Robertson suffered a shoulder injury while on international duty with Scotland which saw him miss Saturday's 2-0 win over Everton, and Klopp confirmed the defender has now undergone surgery.
"All went well, as good as it could be, so rehabilitation starts as soon as he wakes up, I think it happened this morning - we don't know how long it will take."
Liverpool, fourth in the Premier League, take on Nottingham Forest on Sunday, but for now Klopp's focus is solely on Toulouse.
"I haven't thought about Sunday yet, to be honest. Toulouse deserve all of our respect. It's a really interesting story, winning the French Cup last year," he said.
"This year - a really young team, a really talented team... they have a clear idea - but we have to see how they show up here."
Liverpool are top of Group E after wins over LASK and Union Saint-Gilloise. Victory over second-placed Toulouse, currently two points behind, would put Klopp's side firmly on course for qualification for the knockout stage.
"We will make a few changes, not too many, we will see, but the boys have shown already that they are ready for the competition.
"We hope to go long, long, long in this competition, for that we have to make all the decisive steps - and tomorrow night is a very big one."