Kompany arrived after Burnley's relegation from the Premier League last season.
But Eberl, before yesterday's rout of Holstein Kiel, told Sport1: "That is nonsense. The media has always made a ranking list - coach number one, number two, number three.
"My first task after taking office was to find a new coach. You then start to write down a list of coaches who are interesting, who you know, who you have scouted. And then you start to work through this list.
"We received rejections from Julian Nagelsmann and Ralf Rangnick and those were the only two to whom we made an offer."
He "never spoke" with Aston Villa boss Unai Emery, who was also linked.
"After Ralf Rangnick cancelled, we sat down again with everyone involved. Vincent Kompany was on our list of 15 from the start because I think he is a huge coaching talent. He has been on my mind since his time at Anderlecht. I saw him at Burnley. They were promoted to the Premier League with an incredible record of 100 points. And he continued his style of play in the Premier League too, which always impressed me."
In view of Burnley's relegation, Eberl then asked himself, "whether I should present a coach who only has three and a half years of experience and has been relegated?
"At FC Bayern, this naturally raises question marks. I gave him too much weight at the beginning of the coach search, which annoys me now. But in the end I said to myself: 'Come on, fate will show you. He should be the one. And we'll get him to the point where he's a good coach for FC Bayern.'"