The Belgian was rushed to hospital on Friday after collapsing during a reserve-team training session and is expected to be sidelined for weeks. The 40-year-old had been battling a virus in recent days and had missed some training sessions before his collapse.
"I paid him a short visit yesterday," Danks told a press conference ahead of Wednesday's German Cup second round against visitors Magdeburg.
"He is in good spirits. It looks like every day he is getting better. There are no major updates in terms of diagnosis or return to work. Let him rest, let him take his time."
The German champions have a busy match schedule with Magdeburg on Wednesday, followed by the Klassiker against title rivals Borussia Dortmund in the Bundesliga on Saturday. They then travel to Madrid in the Champions League next week to face Atletico.
"We had some good conversations (with Kompany) but kept it away from football and specific tactics," Danks said. "It was just a friendly chat and nice to see him and catch up."
The assistant coach said Kompany's health scare coupled with Monday's Ballon d'Or win for Bayern striker Harry Kane reflected a rollercoaster of emotions for a squad that has shown the necessary team spirit to stay on course.
Kane is the first Englishman to win the prestigious award in 25 years, after Michael Owen won it in 2001.
"For us, we are super professional," Danks said. "Full extremes of life in the last week. Joys and highs for Harry and the lows of the last days."
"To get through these moments we had to rely on our chemistry, our team spirit and that definitely helped us," he added.