Goal's Neil Jones reported last month that Liverpool are not looking to open contract talks with the Spaniard, meaning he will be a free agent come the end of the season.
Moreno, who was highly rated after joining the Reds from Sevilla in 2014, has failed to convince during his time at Anfield.
The 26-year-old has been linked with a whole host of clubs in recent weeks, with Arsenal being unusually tipped to be interested.
However, according to L'Équipe, Marseille's sporting director Andoni Zubizarreta has complied a short-list of targets to strengthen at left-back.
It is reported that Moreno is 'at the top of the list' with the French side looking to upgrade on former Aston Villa left-back Jordan Amavi.
It is expected that Liverpool will look to the Academy once Moreno leaves, with Adam Lewis making waves in the U23s to put himself in the conversation.