Families of the supporters killed in the 1989 tragedy have asked Liverpool Walton MP Steve Rotherham, the city's former Lord Mayor, to put down an Early Day Motion requesting the Queen confer a knighthood on the Scot.
Dalglish was in his first spell as Liverpool manager when 96 fans were crushed to death at the FA Cup semi-final against Nottingham Forest at Sheffield Wednesday's ground.
The 60-year-old earned widespread gratitude and admiration for the role he played representing the city and the club in the aftermath of the disaster.
He attended many funerals in person and remains emotionally involved.
On Friday, Rotherham told a crowd of thousands at a memorial service at Anfield to mark the 22nd anniversary of Hillsborough of the families' request.
Dalglish said: "It is very flattering but I just go about my work, do the best I can.
"If somebody wants to do things that are outside my control that is up to them, but it is very flattering.
"But I don't think I will get carried away with it."
Dalglish resigned as Liverpool boss in 1991, later admitting the stresses associated with Hillsborough had taken a heavy toll.
He returned to the Anfield hotseat for a second time in January following the departure of Roy Hodgson.
Dalglish said: "It was very poignant.
"Everybody that has some feeling for Liverpool Football Club realises the importance of yesterday's day and the service.
"Every single person from the football side of the club were there, the Academy lads were all there for the first time, which was brilliant.
"You tend to forget that it was 22 years ago and some of them weren't born then.
"It is fantastic to see the progress they are making in their quest for some form of justice and I just hope they get it.
"We want to make sure they get what they deserve and I don't think they have had what they deserve so far."