Bayern are desperate to find a high-calibre goalkeeper to fill the gloves of the 39-year-old Kahn who is to draw his legendary career to a close at the end of the season.
Incoming boss Jurgen Klinsmann is understood to be a big fan of Boruc after his impressive performance for Poland against Germany in the 2006 World Cup.
Calls for the Polish international were also supported by Bayern striker Lukas Podolski.
"I would like very much that, after Kahn, we could have Boruc," said Podolski, who was born in Poland. "I want him in the team because he is one of the best goalkeepers in Europe.
"I like to watch him, especially in the Champions League, because they do not show the Scottish league in Germany.
"Also, I would help him from the first day that he would stay at the club."
Any deal for the Celtic keeper is likely to fetch £10million and the fee could rise if Boruc stars in this summer's European Championships.