Reds chief Brendan Rodgers is keen to bolster his attacking options next months, and is thought to have made the Egyptian one of his top targets after he made a trip to assess the player during a midweek clash with Schalke.
Although the Swiss side lost 2-0, the Northern Irishman was impressed by Salah.
The defeat saw Basel eliminated from the Champions League, which serves as a further boost to Rodgers, who may now find it easier to lure the wide-man to Anfield.
His employers are thought to be aware that it may be tough to keep their star man, and are believed to be willing to listen to offers of around £15m.
But Liverpool are hopeful that, with some shrewd negotiating, they can get their target for close to the £12m mark.
Tottenham have also been linked with Salah, but their desire to land a centre-forward may see a move for the North African ace take a back seat.