Sport says the Spanish giants want to use Thursday's Champions League group stage draw in Monaco to hold a meeting with the Merseyside outfit.
Coutinho has risen to the top of Barcelona's shopping list following the departure of his compatriot Neymar to Paris St-Germain.
And to date they have seen three bids, worth £72m, £90m and £118m respectively, for the 25-year-old knocked back by Reds chiefs.
Liverpool's owners, Fenway Sports Group (FSG), insist Coutinho will not be sold and have rejected his transfer request.
Barcelona have made signing the Brazil international their No.1 priority though.