The Italians are keen on the Newcastle United flop.
The French winger is expected to leave the Magpies this summer after a disastrous year at the club since joining last summer.
The Italians were particularly keen on a deal as they eyed him as a replacement for the departing Antonio Candreva.
According to Gazzetta dello Sport, they had already agreed upon a €12 million, around £10 million, fee with Newcastle for his services.
They had also agreed a rough outline of a deal with the player that would see him pick up around €1.5 million per year in wages.
However, a transfer has now moved further away from completion as Ligue 1 side Marseille have revived their interest in the player.
He spent the second half of last season with the French side and would prefer a return there rather than moving to Serie A at this stage of his career.
That leaves Lazio waiting for any sort of signal from Thauvin according to the report, and in the meantime they have begun to identify other potential targets.
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