The German giants were prepared to lose Dayot Upamecano this summer, but Konate followed him out of the exit door when Liverpool triggered his release clause fee.
RB Leipzig need to act in the transfer market and their preferred option is Wolfsburg star Maxence Lacroix.
However, according to German outlet Fussball Transfers, RB Leipzig are also keeping an eye on Ajer.
They view the Norway international as another option this summer as they look to bolster their defensive department before the new Bundesliga season kicks off.
Ajer is expected to move on from Celtic during the ongoing transfer window and has interest from several clubs, including Newcastle United and Norwich City.
He also already has admirers in the Bundesliga in the shape of Bayer Leverkusen.
It remains to be seen if RB Leipzig will turn towards Ajer, but they may need to act quickly given the interest in his services.