The 31-year-old asked to leave the club for personal reasons in January, but was persuaded to stay on Tyneside, with Pardew determined to retain the services of a man who signed a four-year contract extension in March last year.
Argentinian club San Lorenzo, who employ Coloccini's father as a youth coach, are desperate to recruit the central defender, and president Matias Lammens has already indicated he is planning to fly to England in a bid to prise the player away from the Magpies.
However, Press Association Sport understands there has been no contact between the two clubs, and that any approach from the South Americans would not be welcomed.
Pardew has repeatedly spoken of his desire to keep Coloccini, although he admits the decision ultimately lies with the former Deportivo La Coruna man.
However, any deal would be fraught with difficulties with the player still under contract and San Lorenzo having admitted they will not be able to come anywhere near Newcastle's valuation of a man who cost them £10.3million in August 2008.
Coloccini is a fans' favourite and his influence during the tense final few weeks of a difficult season was key, and central defensive partner Steven Taylor is as keen as Pardew to see him stay.
Taylor told the Shields Gazette: "The lads love playing with him and we hope he stays.
"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."
- Sports & Recreation