Following criticism of the Gunners boss by some sections of the club's fans after a fourth season without silverware, which chairman Peter Hill-Wood declared "out of order", Wenger has been linked with a switch to Real Madrid - which may suddenly make the Bernabeu an attractive proposition for someone like Arsenal captain Cesc Fabregas.
However, both the players and the board remain confident Wenger is not about to leave his own "interesting project" at Emirates Stadium any time soon.
"We are not affected [by transfer speculation] and sometimes it is a good thing for us because we make jokes about it when it comes out in the press," Almunia told Spanish sports magazine Don Ballon.
"We say 'did you see that you have signed with Barcelona, once again?' We have a laugh because it is almost always untrue. It is talking for talking.
"Many things are said to sell newspapers, but as far as we are concerned we remain pretty much relaxed."
Wenger has transformed the fortunes of Arsenal since arriving in September 1996, guiding the club to the title three times, including the double twice, and also into the final of 2006 Champions League.
Almunia - signed from Celta Vigo five years ago - has gone on to become one of the most consistent goalkeepers in Europe under the tutelage of the French coach.
The 31-year-old Spaniard, who will soon qualify for a British passport through residency and the possibility of playing for England, is in no doubt of the influence Wenger has been on the squad.
"Working alongside him makes you feel incredibly relaxed and at peace," Almunia said.
"We train hard day in, day out, but he tells us that we will only feel the pressure at the end of the week, during the game.
"We call him the boss. He is the visible face of this club, of Arsenal's project and he is very important for the club."
Wenger continues to champion the potential of his young squad to deliver, the club's last trophy coming back in 2005 with the FA Cup.
However, the Gunners boss accepts the team could do with a couple of experienced heads - arguably in central defence and midfield - before the start of the new campaign, when Arsenal will have to qualify again for the group stages of the Champions League.
Almunia said: "What we are lacking is consistency and regularity, also maybe more experience, not in terms of age but in some aspects of the game, our weak points.
"Playing good football is not always easy and we must adapt our games to the circumstances everywhere we go, and to be a little bit nastier when needed."
Wenger is expected to have to sell in order to increase his summer transfer budget, with rumours suggesting unsettled Togo striker Emmanuel Adebayor - said to be a £25million target for AC Milan, Inter and Chelsea - may well have played his last game for the club.
Defender Kolo Toure, meanwhile, is determined to help Arsenal fight their way back to the top of the table.
The Ivory Coast international is the last regular member of the Invincibles side from 2003/2004 still at the club.
"When you see the atmosphere at Old Trafford after the game, you want to bring that back to your stadium," Toure told Arsenal TV Online.
"I had this feeling five years ago and I want to come back and have this feeling again.
"There is still some work to do and we are such a young team, are improving and I hope that when one trophy comes, a lot will then follow."