Steve Claridge: Liverpool need consistency in their game
Liverpool manager Jurgen Klopp is said to have watched Acheampong, 23, several times over the past few weeks.
Klopp is seeking a solution to Liverpool's left-back problem.
Nathaniel Clyne has taken up the role over recent weeks, with James Milner filling into Clyne's usual right-back position.
The Sun claim Klopp wants the position sorted in January and that a £6million bid would be enough to land Acheampong.
Acheampong joined Anderlecht in 2013, having made his Ghana debut a year earlier.
The star, who is under contract in Belgium until 2019, can also play left wing.
He is due to play for Ghana in the Africa Cup of Nations, which starts next month.
The report adds that Sunderland and Newcastle are also interested in Acheampong, who has scored once in 22 appearances this season.