The 31-year-old asked to leave during the January transfer window and the Magpies are likely to be faced with further interest in him from Argentinian club San Lorenzo.
Coloccini's father is employed as a youth coach by San Lorenzo and club president Matias Lammens has already indicated that he will be travelling to England to try and prise the player away from the Premier League.
Boss Alan Pardew has already stated his desire to keep Coloccini and Taylor is just as keen for him to stay.
Taylor told the Shields Gazette: "The lads love playing with him and we hope he stays. He's a very quiet guy, but when he speaks, he speaks very well.
"Colo and I have had a great partnership over the past few seasons. We have a good understanding. We know each other's strengths and weaknesses. We seem to be able to mix it up.
"He's very composed and he's not shy of a tackle as well. He's been great a guy in training. You can learn a lot from him.
"I've got a fantastic partnership with him, and hopefully that will continue."