The Reds have been tipped to move for the Kosovo international in recent months, while Aston Villa have also been credited with an interest.
Rashica is expected to leave Werder Bremen after the club staved off relegation from the Bundesliga on the final day of the season, but the 24-year-old is supposedly favouring a move to another German club rather than the Premier League.
According to Bild, Rashica has turned down an approach from Liverpool as he looks to secure a move to RB Leipzig.
The report claims that Leipzig are hoping to negotiate a lower fee with Werder Bremen, with Rashica's current release clause set at £33m, and the winger has just under two years left to run on his current deal.
Rashica amassed eight goals and seven assists from 28 Bundesliga outings during the 2019-20 campaign.