The Bundesliga champions parted ways with Niko Kovac on Sunday after a 5-1 thrashing at Eintracht Frankfurt in the league and Ten Hag has been heavily linked to the role.
The coach signed a new contract at Ajax until June 2022 in the close season after leading the club to a league and cup double as well as the Champions League semi-finals.
Ten Hag previously coached Bayern Munich's reserve team between 2013 and 2015.
"I can confirm I feel a strong connection with my team and everyone at Ajax," Ten Hag told reporters ahead of Ajax's Champions League clash with Chelsea.
Coach Erik ten Hag of Ajax during the UEFA Champions League match between Ajax v Tottenham Hotspur at the Johan Cruijff Arena on May 8, 2019 in Amsterdam Netherlands
Image credit: Getty Images
"I can confirm I'm staying at Ajax this season. Bayern is a fantastic club, it is still in my heart, but I'm at Ajax.
"I'm not a dreamer. I focus on Ajax and live for today, and tomorrow's game, which is important."
Bayern are fourth in the Bundesliga, four points behind leaders Borussia Moenchengladbach, while unbeaten Ajax are six points clear at the top of the Eredivisie.
In the Champions League, Ajax are second in Group H, level on six points with first place Chelsea after three games.
"I have a lot of respect for Chelsea but I also trust my players," added Ten Hag. "When they play as a team for 90 minutes we have a chance to win. We will go for it." (Reporting by Rik Sharma Editing by Christian Radnedge)