The winger is currently on-loan at Fenerbahçe but there have reports that recently appointed manager Jurgen Klopp wants to recall the Serbian international in January.
The Daily Mail claim that Klopp is keen on bringing Markovic back but he will have to wait until the end of the season.
The Serbian international was loaned out to Fenerbahçe over the summer transfer window and has already established himself as an important member of the team.
Markovic was signed during the Rodgers era for a £20 million fee from Benfica in the summer of 2014.
Rodgers was sacked following the 1-1 draw against Everton in the Merseyside derby and replaced by German manager Jurgen Klopp.
Markovic is expected to start for Fenerbahçe against Ajax in the Europa League midweek and against Galatasaray in the Intercontinental derby on the weekend.