Regardless of these fresh fitness concerns, rotation is something that will have been on Klopp's mind as the trip to Huddersfield kick-starts a run of six games in 23 days for his Liverpool side.
Sadio Mane, who reportedly broke his left thumb on global duty for Senegal, underwent surgery on Wednesday, Liverpool confirmed.
Mane reportedly broke his thumb in training prior to his country's Africa Cup of Nations qualifier against Sudan on Tuesday.
Virgil van Dijk is also on Liverpool's lengthy list of injury issues, although Netherlands boss Ronald Koeman is confident the centre-back's rib complaint will not force him to sit out any club games.
Neither player took part in Thursday's session at Melwood, although James Milner did return to the track nearly two weeks on from hobbling off in the scoreless draw with Manchester City.
With Liverpool's attack misfiring and their creativity having been lacking in some games, the return of Lallana could be particularly important as the England play-maker looks to overcome the injury woes that have plagued his last 18 months.
"I know Juergen long enough that I know he loves to use some smokescreens", Wagner, who coached the second team at Borussia Dortmund when Klopp was in charge of the senior side, told a news conference.
Jurgen Klopp has been impressed with the player's attitude this year and his performances have led many to suggest that he should be starting ahead of Mo Salah. I have known him long enough and he likes to moan after the global break!
Wagner said Saturday's match represented a chance to build on a 1-1 draw at Burnley last time out. So why should we give it out there to the world?