Babel looked as though he was heading for Bundesliga side Hoffenheim after the clubs agreed a fee.
However the proposed move has broken down, with Babel earlier indicating he would prefer to join Ajax.
There is speculation the Dutch side's £20million-rated striker Luis Suarez could be heading for Liverpool but whether Babel might be part of the deal remains to be seen.
When asked about the player's situation, Dalglish said: "He is staying here."
