The winger has endured a torrid spell back in Portugal with Sporting Lisbon so far this term.
His season-long loan deal could be terminated, having made just 11 appearances in all competitions and not played since early December.
Marco Silva is keen to add more new faces to his Hull squad before the end of the transfer window to strengthen their chances of survival.
Liverpool loanee Lazar Markovic has scored two goals for Sporting Lisbon since joining them on loan
An agreement with Sporting must be reached first
According to ESPN FC, Liverpool are open to the prospect of sending Markovic to the Premier League outfit, but an agreement with Sporting must be reached first.
Liverpool are willing to cancel the 22-year-old’s stay at Sporting, although a move to Hull needs to be in the pipeline first.
Markovic will not be returning to Anfield this month, as the attacker failed to impress Jurgen Klopp during pre-season.
But the Reds will hope their £20million signing, who arrived in 2014, can potentially kickstart his career in England at Hull.
Marco Silva is eyeing more January signings at Hull
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Jurgen Klopp was not impressed by Lazar Markovic during pre-season at Liverpool
The Sun claim though in order to get Markovic off their books, Sporting are required to make two payments totalling £1m over the season.
They are considering paying that early though to offload the ex-Benfica man.
Beyond this term, Markovic may not have a future in England as his current contract at Anfield expires in June 2017.