The winger could be set to link up with his former manager Jorge Jesus.
Markovic joined Liverpool in July 2014, with Brendan Rodgers paying £20 million for his services.
He made 19 appearances in his first season at the club but failed to impress with a series of disappointing displays as Liverpool struggled.
Last season saw him loaned out to Fenerbahce but the Turkish side have opted against making that move a permanent one this summer.
According to Record however, he may have a new option as Sporting Lisbon are interested in securing his signature.
They report that manager Jorge Jesus is keen on bringing Markovic to the club and reuniting with him this summer.
The two previously worked together at Benfica, where Markovic was one of their star men when they won the treble in Portugal in 2014.
So far a price for the Serbian has not been mentioned, although it is likely Liverpool would be determined to recoup much of what they originally paid for him.
It is also unknown whether Markovic would be interested in the switch; especially considering his association with rivals Benfica.