Coloccini is locked in contract negotiations with United that now may be mothballed until the end of the season, according to boss Alan Pardew.
"I have known Fabricio for a number of years, I know exactly what kind of player he is," Gutierrez told the Sunday Sun.
"Maybe in the first season he was bad. But it was bad for all of the players who arrived here because we were relegated.
"But I know the qualities that he has. He always tries to play the quality pass and he's a really, really good defender too.
"I am so glad that he is here with our club and yes, of course I would like him to stay and I said that to him."