The 24 year old has already scored seven goals in 12 games for the Reds so far this term, but the Uruguay international has also been accused of diving by Manchester United counterpart Sir Alex Ferguson and racism by their defender Patrice Evra.
"He has been fantastic and the great thing about him is that he is very unassuming as well," Dalglish said.
"Everybody can see what he can do on the pitch, but he has got no edge to him. He doesn't think he is better than anyone else.
"He is a great ambassador for the football club. For us, as well as his football, the other things he brings to the club are very important as well.
"He is just a fantastic person as well as a fantastic footballer.
"As I have said before, he has only been here since January and already we are running out of compliments to pay him, which I suppose is a huge compliment in itself."