A group of disgruntled supporters are planning to stage a protest against the 53-year-old coach at St James' Park ahead of Saturday's clash in the Premier League.
Calls for Pardew to be sacked have come from a number of fans following the manager's failure to guide Newcastle to victory in their first four games of the league season.
In Coloccini's programme notes, the defender wrote: "It will not be an easy game because Hull are a good team. It is very important that you are right behind us and support the team and the players who are on the pitch.
"You want to win every game, just like us, and we all want the best for this football club. We are football fans too, so we understand that things can get frustrating. But please, support the team for 90 minutes inside the stadium. We need your support.
"We have a lot of new players and a young squad. They need your backing, a push from you and a positive atmosphere to get the best out of them. Hopefully, you can cheer us on to three points and that will give our season a real boost."
The Magpies are currently at the bottom of the league table.