Meanwhile, Milner was forced to sit out of the Reds' 3-2 win over West Ham on Monday with a muscle strain and Shaqiri has been out of action since January due to a calf injury.
Klopp provided an update on the trio during his pre-Watford press conference, confirming they are getting "closer" to returning but will remain sidelined from the trip to Vicarage Road.
“[They are] all coming closer, much closer,” the Reds boss told reporters.
“Hendo is running, Millie is running and even more. It was not enough for this game now, but we will see – especially with Millie – what we can do for Tuesday.
“I'm not sure about Hendo, and Shaq not yet, but they are all coming closer.”
Klopp's squad is largely in good shape heading into the latter stages of the season, but the return of Milner and Henderson, in particular, will be welcome news.
The skipper's absence was certainly felt in Liverpool's 3-2 comeback win over West Ham on Monday, with left-back Andy Robertson emphasising that fact after the game.
“When you don't have your captain out there you can feel it,” he said.
“Hendo is a real leader. He was in the changing room before saying a few words and he was exactly the same as he always is before games, and he was in there again afterwards.
“It was good having him there. Everyone hates being on the sidelines and Hendo is no different. The quicker he's back the better for all of us.”