Sky sources understand Liverpool have held talks with forwards Roberto Firmino, Carlos Bacca and Salomon Rondon - and a deal for Firmino could be completed in the next 24 hours.
The club have widened their search for a new striker to three South American targets after deeming Christian Benteke's £32.5million asking price too expensive.
The striker is currently on Copa America duty with Brazil and is seen as an ideal replacement for Raheem Sterling – should he leave the club – with his ability to play across the front three.
Bacca is another player on Liverpool’s radar due to his prolific form for Sevilla and Colombia.
It is believed he would command a fee in the region of £20m. He scored 28 goals last season, including two goals in the Europa League final.
Sky Sports' Spanish football expert Guillem Balague recently said that Bacca wants to leave Sevilla and is open to a move to the Premier League.
“Carlos Bacca at the end of the season told Sevilla he would like a way out,” Balague told Sky Sports News HQ.
“Sevilla would like him to stay, but he does know there is interest from the Premier League and Italy.
"He likes the idea of coming to the Premier League, of course he has been abroad for a few years and would be happy to continue that progression abroad."
Liverpool are also pursuing Rondon, who plays for Zenit St Petersburg and represents Venezuela at international level.
Rondon, who would cost £15m, scored 20 times last season as Zenit won the Russian title.
Liverpool have also been linked in the media with Monaco centre-back Aymen Abdennour but Sky Sports News HQ has been told they do not intend to make a move for the player.
Sky Sports News HQ also understands there is currently no interest in Inter Milan's attacking midfielder Mateo Kovacic and as of yet there has not been a second bid made for Southampton defender Nathaniel Clyne.