Premier League side Southampton, Turkish side Galatasaray and Spanish Sevilla have been reported to be among the suitors for the 26-year-old centre-back.
Sakho's off-field struggles began in April 2016 when he was handed a 30-day suspension by UEFA for testing positive for a substance which was understood to be a fat-burner, following a Europa League match.
The central defender, who arrived at Liverpool three years ago, is currently training with their under-23 squad.