Dutchman looked set to move to Hoffenheim
The move to Germany looked very likely as the Anfield outfit accepted a bid of around £6 million for the Dutchman and even went as far as having a medical, but it seems the deal collapsed on personal terms between the player and the proposed club.
Babel also showed a willingness to be part of a deal that would see him go back to former club Ajax, with Luis Suarez moving in the oppposite direction, but it remains to be seen if any light will be shed on such a deal.
Dalglish would not speculate on how long Babel would be at the club, saying: "He's staying here."
The Reds have been linked with a move for Blackpool captain Charlie Adam, but Dalglish refused to be drawn on any possible transfer targets.
"If we have some business to discuss we will discuss it," he added.
"We will try to adopt the way of Liverpool Football Club and certainly one of our ways is to be respectful of other clubs and certain players at other clubs.
"The most important people we have are the people at this club."