The highly rated German youngster hasn’t been playing regularly for the Bundesliga side, who have taken everyone by surprise this season.
Sportbild say Leicester City and Stoke City are keen on a winter transfer, but could face competition from Bayer Leverkusen and Borrusia Monchengladbach.
Leipzig aren’t too keen on selling Selke at the moment, despite him featuring rarely, but could be tempted by an offer in the region of €15m-€20m.
Both Leicester and Stoke have struggled to score goals this season, and are expected to be active in the transfer market.
However, it remains to be seen if there is a genuine interest from either of the Premier League clubs, as Selke might not be the quick fix they need at the moment.
The 21-year-old signed for Leipzig last summer in a €8m deal from Werder Bremen, and has a contract until 2020.