Newcastle's 'Three Amigos' have all been linked with a possible move away from St James' Park in the close season, with Enrique's future looking particularly uncertain as he heads towards the final 12 months of his current contract.
Gutierrez has been interesting top-flight clubs in both Italy and Spain, but the Argentinian, who still has two-and-a-half years of his own deal to run, is determined to remain on Tyneside next season.
However, he is worried about the possible effect of losing either Enrique or Coloccini, two of the Magpies' most effective performers in the current campaign.
The trio have become close friends since linking up in the summer of 2008, and Gutierrez is desperate to see their on-field relationship continuing for as long as possible.
"I am happy here, and yes I do want to stay," said the South American. "My family is happy as well. The only issue is that the club has to decide what it wants to do next season. We do not want to be back in a position where we have problems with relegation.
"We are in a good position at the moment, with the players to make a strong team, but we need to add a few more to make sure we continue to move forward.
"We also need to make sure people like Jose and Fabricio stay. They are my best friends but they are also very important players. We are all part of a group, and it is important that group stays together.
"Sometimes, things happen that mean it is very difficult for a player to stay. Look at Andy Carroll in January - £35m, Liverpool, that is difficult for the club and the player to turn down.
"That is football. But in general, I want all of the players at this club to stay. That will make it much easier for the team to be strong next season."
Newcastle's strength in the current campaign is underlined by their tally of 35 Premier League points, already an improvement on their total from the whole of the 2008-09 campaign that ended in relegation.
Gutierrez is the only player to have featured in all 27 league matches so far, and having struggled to adapt to the pace and style of the Premier League in his first season in England, the 27-year-old now appears much more at home amid the cut and thrust of the top-flight.
His left-wing relationship with Enrique is one of Newcastle's principal attacking strengths, and his measured delivery from the flanks has been a key factor in Leon Best's emergence in the last two months.
"I feel a lot more comfortable in the Premier League than I did in my first season here," said Gutierrez. "It feels normal to be playing at this level now. My first year was difficult, and not just for me. We had five managers and there was a lot to contend with.
"This year, I feel really good in the Premier League. In the first year, it was tough, because we went down. The second year was not really the same, but we were in the Championship. This year has been good because I feel like I have played well back in the Premier League."
The only thing that has been missing from Gutierrez's play is success in front of goal, and the subsequent Spiderman celebration that so captivated supporters during last season's victories over Barnsley and Blackpool.
The winger has scored once this season, in October's 2-1 defeat at Manchester City, but bizarrely the strike coincided with the first time he had decided not to take his mask onto the field with him.
The goal sparked a run of games where Gutierrez was mask-less, but having failed to find the target since, the Spiderman skull cap will be back within easy reach when Bolton visit Gallowgate tomorrow.
"The mask is still around," he said. "The first time I didn't take it onto the pitch with me, I scored at Manchester City. I then went on a bit of a run where I didn't take it with me, because I was hoping that would make me score more. That hasn't really happened, so it's probably time to get the mask back for every game.
"Normally, I have the mask at every home game, but decide about the away matches on the day of the game. Maybe for a bit now though, I will take it with me all the time."
* Three of Newcastle's matches have been moved to accommodate coverage on live television.
The trip to Aston Villa has been put back 24 hours to Sunday, April 10 (ko 4pm), while the visit to Liverpool, and a potential reunion with former striker Andy Carroll, will now take place on Sunday, May 1 (ko 12pm).
The home game with Manchester United on Saturday, April 16 will now kick off at 12.45pm, although the game will be moved entirely if Sir Alex Ferguson's side reach the semi-finals of the FA Cup.
* Newcastle's junior side secured a 2-2 draw with Club Nacional in their second game of the Copa Carnevale youth tournament in Italy yesterday afternoon.
Having lost their opening game to Fiorentina, Peter Beardsley's side, which includes the likes of Ole Soderberg, Phil Airey and Joan Edmundsson, faces an uphill battle to qualify for the knock-out stages ahead of tomorrow's final group game against Lecce.