The English newspaper claim that the 23-year-old is willing to discuss a potential move to Wales as he has failed to feature once under Jurgen Klopp this season and wants regular first-team football.
Markovic has not only struggled to break into the first-team this year but it has been a recurrent theme since sealing his £22.5m move from Benfica in 2014.
The Serbian has already been sent out on loan three times: to Fenerbahce in 2015-16, Sporting CP in the first-half of 2016-17 and Hull City in 2017.
This lack of consistency has hindered his development and will be a decisive factor in any decision made about his future.
Markovic would also be a good addition to Carvahal's squad who are currently bottom of the Premier League and in need of some new attacking threat.