Liverpool's owners, Fenway Sports Group, have only appointed Dalglish until the end of the season.
Long term it is understood they want a younger man at the Anfield helm.
However, Dalglish, who was on holiday in Dubai when asked to become manager by John W Henry, told a press conference on Monday when he was officially unveiled: "I have heard stories about demanding this and demanding that.
"(But) when I was phoned early on Saturday morning, when I was away, and was asked if I would take the job, it was a straightforward yes and that was it for me.
"There are no conditions, there are no clauses. I came back here to work at a club that myself and my family are eternally grateful for many things they have done for us.
"When I was asked to do it, there was no way I was going to be disrespectful and say no."
Dalglish then joked: "If I can get to the end of the season, then I will probably end up as one of the longest-serving managers in the Premiership.
"We'll not start running before we can walk."
The Scots first Premier League game in charge will be Wednesday's trip to Blackpool.