For a number of weeks, the Spaniard has been heavily linked with a switch to Anfield during the summer transfer window.
With less than a year remaining on his contract, the 29-year-old is said to be available for a fee in the region of £30m.
However, according to the Liverpool Echo, the Premier League champions are not actively pursuing a deal for the playmaker.
The report comes after it was recently suggested that Liverpool would have to sell at least one more player to accommodate Thiago's arrival.
Paris Saint-Germain are said to be monitoring the situation.