The Catalan giants believe Liverpool would find it difficult to turn down an offer in the region of £89m (€100m).
Barca also believe that although Coutinho loves Liverpool, a Brazilian player would find it difficult to turn down Barcelona.
Liverpool’s position has not changed – he is not for sale and he is staying.
Liverpool are under no pressure to sell, especially because Coutinho signed a new five-year contract in January.
Barcelona have already had a £72m bid turned down for the 25-year-old but are planning to return with an improved offer, Sky sources understand.
Neymar is wanted by Paris Saint-Germain and Sky Sports News have been told there is a 90 per cent chance that deal could happen.
Coutinho has developed into one of the top players in the Premier League during his five seasons at Anfield and is viewed as a viable replacement for his international team-mate at the Nou Camp.