The Argentine defender, 32, has been linked with moves away since asking to quit the club and return to his homeland in January last year.
Coloccini has returned to South America on several occasions since, but continues to put in strong performances for Pardew's side.
The centre-back is contracted until June 2016 and Pardew said he was hopeful Coloccini would choose to stay at Newcastle.
"I'm not worried about it at this stage, but obviously it is a conversation that I will have with 'Colo' and we will pick the right decision for the club," Pardew said ahead of his side's clash against Everton on Tuesday.
"What might be right for him might not be right for the club, but I am hoping we both make the same decision because I want him to stay.
"He is an essential part of this team, one of my most important players.
"I don't see anything to give me cause for alarm, if I am honest. His mentality for the game will never change.
"He is quite calm. He enters the game to be the best player - and most of the time he is."
