It was reported first-team coach Primorac was set to take a job in Turkey prompting further questions about whether Wenger will bring his reign at Arsenal to end this summer.
Primorac has worked with Wenger at Arsenal for the past two decades and is one of his most trusted members of his backroom team.
Wenger also worked with Primorac in Japan with Nagoya Grampus Eight and the speculation about one of his loyal assistants had raised fresh doubts over his future.
However, Wenger, who has been offered a two-year contract extension but is yet to decide his future, has described reports that Primorac is leaving Arsenal as “fake news”.
“That is a complete invention,” he said. “Today you say anything and everybody takes it without checking any information.
“Everybody takes it and makes a subject of it. It is not serious.”
Arsenal, who face West Brom at The Hawthorns on Saturday, are five points outside of the top four and facing a fight to qualify for the Champions League.
The Gunners are in the semi-finals of the FA Cup and Wenger was asked what would be considered as success for the club this season.
“It is not down to me to judge that,” he said. “Our job is to do as well as we can until the end of the season. If we want to play in the Champions League next season we have a tough job because we have six or seven teams fighting for the places.
“How well we do until the end of the season will depend on that. We are in the semi-final of the FA Cup and we have an opportunity there as well.
“They are our targets. Success is to take the maximum out of the potential of the team.”
Arsenal have qualified for the Champions League in every since Wenger took over. He confirmed the players will lose out on bonuses if they fail to finish in the top four this season.
“If you do not achieve you do not get the bonuses,” he said.
Asked whether qualifying for the Champions League is the minimum requirement for Arsenal this season, Wenger added: “Look, nothing is good enough any more. So you try to do as well as you can.”
Arsenal have two games in hand on Liverpool and one game in hand on Manchester City and Tottenham, who are six points above them.
Wenger admits they cannot afford to lose further ground on the teams above them this weekend.
“It is vital, of course,” he said. “It is a strange championship because there is no continuity at the moment. We have had games cancelled, after you play away, you do not play, you play in the FA Cup and you play away again. So you do not really know where you stand.
“You do not have the same number of games, you do not have the continuity home and away. What is for sure is that we are in a position where we cannot waste points.”
Alex Oxlade-Chamberlain was having his hamstring injury assessed today and is a doubt for the West Brom game. West Brom have already reached 40 points under Tony Pulis and Wenger is wary of the threat that they will pose from set-pieces this weekend.
“They have a lot of experience, are well organised, physically very strong and are very efficient on set-pieces,” he said. “I think they are the team who have scored more goals than anybody else on set-pieces.”