The 18-year-old has made five appearances for the Ligue 1 club in a breakthrough 2019/20 season.
Andy Robertson has been Liverpool’s only senior left-back since Alberto Moreno’s departure to Villarreal in July.
Midfielder James Milner filled in for the rested Robertson in Saturday’s 2-0 win over Watford.
French newspaper L’Equipe say Liverpool could make Goncalves, who made his senior Toulouse debut against Paris Saint-Germain in August, their next young signing.
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The Reds signed highly-rated 16-year-old midfielder Harvey Elliott and 17-year-old defender Sepp van den Berg in the summer.
Both players have featured prominently in Liverpool’s Carabao Cup campaign this term.