With Jamie Carragher retiring at the end of the season and Rodgers still unsure about Martin Skrtel, Williams is top of Liverpool's wanted list this summer. Rodgers admired the 28-year-old enough to make him skipper in his two years at the Liberty.
"Of course I want him to stay - he's so important to our team," Laudrup said. "Ashley has done so well for us. He had a difficult start to the season but it shows his character that he's come back to play at such a high level for the past three months.
"He has so many good qualities. He's quick, strong, his positional play is good and he reads the game so well.
"It's also so important that he is good on the ball because that gives confidence to the rest of the team.
"I can understand the bigger clubs looking at him. If they want your players, it shows they are performing. We don't want him going anywhere."