Winger Gutierrez put an end to speculation regarding his future yesterday by signing a fresh four-year contract with the Magpies.
Reports have suggested that manager Alan Pardew now wants Coloccini's long-term future sorted and compatriot Gutierrez believes that he will not take much persuading.
"Colo and I love life at Newcastle and want to spend our best years here," Gutierrez told the Evening Chronicle.
"Since Newcastle returned to the Premier League, Colo has been in great form. This wasn't a surprise for me because I played against him many times in La Liga when he was at Deportivo and I was at Real Mallorca.
"He is a very important player for us. He is doing really well as captain and he has a big experience of playing in first-class matches."
Coloccini joined Newcastle in 2008 for a fee of £10.3m.