Mamadou Sakho has been offered a new long-term contract by Liverpool in an attempt to prevent him from leaving Anfield.
The Reds are moving to try to keep the France international centre-back amid interest from European clubs, sources have told ESPN FC.
Sakho has not been in the matchday squad for either of Liverpool's opening two Premier League matches and is concerned about his prospects for regular games this season.
But Roma's recent offer to take him on a season's-long loan was rejected, while Bayer Leverkusen's interest has also received no encouragement.
Manager Brendan Rodgers does not want to sell the 25-year-old, who he sees as an integral part of his squad.
Dejan Lovren was chosen ahead of Sakho to partner Martin Skrtel in central defence as Liverpool opened their Premier League campaign with 1-0 victories over Stoke and Bournemouth. Kolo Toure was named as the back-up on the bench for both games.
Sakho left Paris Saint-Germain for Liverpool in 2013 because he felt he was not getting enough games and is keen to ensure he plays regularly enough this season to secure a place in host nation France's Euro 2016 squad.
He is expected to wait to see whether he gets more first-team chances over the coming weeks before deciding whether to accept the deal.