The Bundesliga giants recently snapped up former-Barcelona boss Pep Guardiola, and the Spaniard will replace Jupp Heynckes at the end of the season.
But Hoeness revealed Bayern Munich have considered Wenger in the past, only the Frenchman spurned their advances.
Speaking to The Sun, Hoeness said: "We did try to get him at Bayern Munich a few times. Even before he went to Japan (in 1995), Franz Beckenbauer and I went to Nice and discussed with him and everything was clear, but then at the end of the day he decided to go to Japan.
"We were very surprised. From Japan he went to Arsenal and over the years, whenever we were looking for a new coach, Wenger was always one considered.
"He's a very serious person, very strong and has a very good idea about the game. There have been a few moments where we have discussed his name over the years.
"He has always remained loyal to Arsenal which is fantastic behaviour. But it is true we wanted him at Bayern a few times."
Arsenal face Bayern Munich in the second-leg of their Champions League last-16 tie on Wednesday, hoping to overturn a 3-1 first-leg deficit.
The Premier League side were outclassed at the Emirates Stadium, and face a mountain to climb to progress to the quarter-finals.
The 2010 and 2012 finalists will be hoping to go one better this season, and win their first Champions League trophy since 2001.
The German giants are runaway leaders in the Bundesliga, and are one of the favourites to win the continental title this term.