The report states that the Yellow Canaries have made an enquiry regarding the availability of Markovic.
The Serbian international missed 29 games through injury this season but did manage to recover in time for the Turkish Cup final against Galatasaray last week.
The former Benfica man missed 140 days due to injuries over the course of the season but did play regularly for Fenerbahce when he was fit.
Markovic featured in the final but picked up another injury shortly after and will miss the European Championships in France this summer as a result.
Liverpool boss Jurgen Klopp has told Markovic that he has a chance to prove himself over pre-season and could end up being kept on next season.
Markovic joined the Reds on a big money move the season before last but struggled under the stewardship of former manager Brendan Rodgers.