Bayern currently sit sixth in the Bundesliga table, having lost back-to-back games, allowing Dortmund to seize top spot after seven games of the new campaign.
The poor run of form has increased pressure on new head coach Niko Kovac, who was chosen as the long-term successor to Jupp Heynckes despite just one trophy win before moving to Munich.
However, Delaney has urged caution in writing off Bayern this early in the season, referring back to last season when they started poorly before righting the ship and then winning the league by 21 points ahead of Schalke and another eight clear of Hoffenheim and Dortmund.
He is also refusing to get carried away with Dortmund's own strong start, saying that BVB must continue to build under new boss Lucien Favre.
"I think we only have to go back one year and we will see the same situation for Bayern Munich," Delaney told Goal. "It is too early to say that [there is a crisis].
"I wouldn't stand here and say that we now go for the title. Of course, we have done well. We have sometimes been a little bit lucky, we had the results with us.
"But in the end, we are a new team, there are a lot of new guys, a lot of young guys, a new coach, but we are very satisfied so far."
Delaney is also a new arrival at the Westfalenstadion following a €20 million (£17.5m/$23m) summer transfer from Werder Bremen and has been impressed with what he has seen so far despite the step up in quality.
Favre has tried to get his young players playing an attractive attacking style of football, with Jadon Sancho and Christian Pulisic being singled out by Delaney for praise after their excellent starts to the 2018-19 campaign.
"It's good. It's a different level. It's been challenging," the 27-year-old admitted. "You talk a lot about how it's easier to play football for a good team, but there is also more expected from you. I feel that. There are very good players there.
"We have an 18-year-old who plays for the England national team in Jadon Sancho, Christian Pulisic has 100 games in the Bundesliga and is just 20-years-old. We have an amazing bunch of not only young guys, but young guys with great talent."
The Denmark international has played in six of seven league games so far this season, earning rave reviews for his performances, but is aware of the midfield depth at Dortmund and knows he will have to keep working hard to keep his place in the side.
"It is difficult," he continued. "You see a lot of rotation due to the talent we have. If you look at the holding six-eight position, we maybe have four players who are more or less equal and more or less in the same boat not just in their own personal opinion but by the club, and they all think they should play because of what they have done.
"You have [Mahmoud] Dahoud, you have [Julian] Weigl who have both been dominant in the league. You have [Axel] Witsel who plays in the Belgium national team and me, and we're a little bit older. It's a tough situation, but it's very nice to be a part of."