Manager Jurgen Klopp is believed to be on the lookout for attacking reinforcements as he aims to bolster his Reds squad during the current January transfer window.
Praet has netted 23 goals in 154 appearances for Anderlecht since making his senior debut for the club back in 2011.
And according to the Daily Mirror, Liverpool are ready to compete with Serie A side Fiorentina to land the Belgium international this month.
Attacking midfielder Praet is said to be valued at around £22.5m by Anderlecht, and Liverpool chiefs are prepared to sanction the move, the British newspaper reports.
Liverpool, who are currently struggling with a number of injuries, were held to a 2-2 draw by Exeter in the FA Cup third round on Friday night.
The Reds are now preparing for their crunch Premier League clash with Arsenal at Anfield on Wednesday night.
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