Thiago has not played for Liverpool since October 17, when he suffered an injury during the Merseyside derby draw with Everton.
The Spanish midfielder excited fans by returning to training this week but Klopp says he is still working his way up to full fitness and will miss Sunday’s match against West Brom.
The Premier League champions could welcome back Milner and Shaqiri, however, with both returning to full training recently.
Klopp said: ‘So Thiago has made his first step towards team training, he wasn’t involved in the full session but he’s making good steps.
‘Unfortunately for him he had long time out so we cannot rush it and we will not rush it.
‘The other guys are closer. Shaq [Shaqiri] trained really good and Milly [Milner] yesterday had a full session.
‘We still have two more training days before we need to make a decision but Thiago will not be involved.’
More to follow…