Reports in England and Germany, including the Bild newspaper and Kicker magazine, claim the Bundesliga club have held talks with Wagner about him replacing Ismael during the league’s winter break.
Ismael was appointed on a full-time basis less than two months ago, as a replacement for Dieter Hecking - but the Wolves have won just two of eight games under his guidance and are only a point above the bottom three.
The Frenchman will lead them in their final Bundesliga fixture of 2016 against Borussia Monchengladbach on Tuesday but - according to reports - he could then be replaced by Wagner.
However, Bode, who is also Volkswagen’s vice-president of communications, says this is not the view of Wolfsburg’s board of directors.
“We have a coach who is currently showing that he can give this team new direction,” he told Germany’s dpa agency.
“Last weekend’s result shows that the team has taken up the fight. We are playing Gladbach on Tuesday and nothing is going to happen to the coach either before or after that game.”
Ismael was angered by the persistent speculation about his future at the weekend, snapping at reporters during the post-match press conference after a 1-0 win over Eintracht Frankfurt.
He said: “It’s just getting on my nerves. If we lose a game then there are questions about my future - but they come even when we win a game.”
Wagner, 45, took over at Huddersfield in November 2015. The Terriers are currently in the play-off positions in the Sky Bet Championship after three successive wins.
Meanwhile, Monchengladbach coach Andre Schubert is also reportedly on the brink of losing his job, with one or potentially both set to be ousted following Tuesday’s Bundesliga match.