Mirror Football understands that the Reds have settled on an agreement for the Brazilian for an initial fee of €120million (£106.4m), with a further €40m (£35.5m) in add-ons.
It is the second-most expensive transfer of all-time, trailing the £198million PSG paid Barcelona for Neymar last summer - and it is the most money ever received by an English club.
Coutinho will pen a five-year deal, with the Catalan giants likely to give him an extension in the summer to ensure his deal does not run out mid-season.
He was spotted in London on Saturday preparing to jet to Barcelona and link up with his new club.