Manager Roberto Martinez admits he is happy to be linked to jobs at bigger clubs but insists there is still work to do at Wigan.
The latest speculation suggests the Spaniard, who masterminded the Latics' Premier League survival from a seemingly-doomed position and signed off with a 3-2 home win over Wolves, is being considered by Liverpool's owners.
And Martinez is happy that he is being talked about for doing a good job.
"There is another manager in that club [Liverpool], no? When you get stories linking clubs with your players or in this case with a manager, it must be because you have done something right.
"We cannot control speculation and I am not going to lie to you, I like the speculation. I see it as a real compliment. Speculation will follow a team - you get good speculation and bad speculation.
"The speculation I don't like is when it suggests you are going to lose your job after a couple of defeats. I am proud and happy that the club are attracting a lot of good headlines and stories."
Reacting to rumors that he will be replaced next season by Wigan Athletic's Roberto Martinez, Dalglish said, "I expect the owners to have more dignity and integrity than to believe a story in a newspaper."