The Daily Mail says Koscielny is a top summer target as Pep Guardiola prepares to take over at the German champions.
The Bundesliga club are expected to lose veteran Belgian centre-back Daniel van Buyten and are keen to strengthen with someone of who would be comfortable with the incoming boss' style.
Koscielny was tracked by Barcelona during Guardiola's final season in Spain and his since continued to go from strength to strength since his arrival in north London three years ago.
"I still have four years left on my contract after June," he explained. "I feel good in the club - they have faith in me. I'm happy in London, my family too. I'm not thinking about [leaving]."