The Reds hierarchy are working on several options to bolster their attack in the summer transfer market amid ongoing interest in Bradley Barcola and Yan Diomande.
Liverpool's main barrier to a deal is PSG, with the 24-year-old emerging as a priority target for the defending European champions, who have already reportedly seen three offers rejected.
French outlet L'Equipe claim PSG will now make a fourth and final bid - on the back of Akliouche scoring six goals and laying on six assists in 21 Ligue 1 appearances last season - but Monaco are holding out for around €70M.
Monaco's own financial issues mean the club need to raise around €150M overall from summer sales and Akliouche's exit can help them towards that target.
Liverpool have refrained from an official bid up to this point, as they monitor PSG, but with a deal edging closer now - Andoni Iraola must decide whether to launch a last minute challenge or focus on other targets.