The 30-year-old Argentina international has not submitted a formal transfer request, but has indicated his desire to return to South America for personal reasons.
That has alerted the likes of San Lorenzo, who upped the stakes today when president Matias Lammens told ESPN Radio Rivadavia: "Time is running out for the signing.
"When you go for a class A defender, the timings are a bit different, but if in the next week we don't have a response then we will have to go for another option."
Lammens' comments will infuriate the Magpies as they attempt to persuade Coloccini,
who signed a four-year contract extension in March last year, that his future remains at St James' Park.
The club has not commented on rumours that Coloccini wants to leave after they resurfaced today.
His father Osvaldo revealed San Lorenzo's interest in the player several days ago, and they have made little secret of their intent to sign him despite admitting they cannot afford to buy him.
Lammens added: "Coloccini's arrival is very difficult. We can't go out and buy him; we have always said that we depended on the desire of the player to rescind [his deal].
"We can offer him a very good contract in the case of him rescinding, but San Lorenzo have nothing left to do with regards to the negotiating."
Coloccini cost Newcastle £10.3million when they signed him from Deportivo la Coruna during the summer of 2008.
He struggled initially to settle into English football and was part of the squad which was relegated at the end of his first season.
However, he has since rebuilt his reputation to the extent that he was handed the armband by manager Alan Pardew following Kevin Nolan's departure for West Ham and led the club to fifth place in last season's Barclays Premier League.
Coloccini's form has been patchy in recent weeks amid a run which has seen the Magpies lose 11 of their past 14 games in all competitions to slide towards the relegation zone and out of the FA Cup.
Speaking about the FA Cup loss to Brighton, Pardew said: "It was a difficult situation. It was a really horrible day for the players and fans and more importantly the staff, but we have to lick our wounds.
"We are much stronger this week and that is much better for us."
Despite more frustration in his search for a striker to replace the departed Demba Ba, Pardew has had some welcome good news with the arrival of French full-back Mathieu Debuchy and the return to fitness of Papiss Cisse and Yohan Cabaye.
Pardew knows his big names will be needed to end a dismal run of just four points from 10 away league games this season.
Ahead of tomorrow's trip to Norwich he added: "We are getting some senior bodies back around the team at a crucial time.
"We really need to get some momentum back for our fans, who we really let down last week. It is important that we give a really good account of ourselves at Norwich and start getting points on the board.
"We have been very competitive and we just need that break to give us the win and the good feeling in the group.
"I don't think we're a million miles away from that. Certainly the team that played last week was a shadow of the one that will line up at Norwich."
Pardew believes midfielder Cabaye will be key to his side's recovery, and although the Frenchman is likely to start on the bench at Carrow Road, his influence when injury free could significantly dictate his side's fortunes for the rest of the season.
"At the start of the season we were unaware Yohan was carrying an injury and so it didn't look like he was playing his best football for us, certainly not as well as he had been playing at the end of last year," Pardew added.
"But he looks much better now. His movement and passing is better and he is going to make a big, big difference for us because so much of our play goes through him. So he will make us a more attractive team and hopefully a more productive team."