The Brazilian completed a move to Camp Nou on Monday for a deal that has widely been reported as costing in the region of £142m.
Barca's vice-resident Jordi Mestre recently suggested that the club paid less than what was reported during their failed pursuit of the player in the summer.
"The club has always been interested in signing Coutinho, the difference to last summer is that there was a big cut in price," Mestre told reporters. "We won't state the numbers because Liverpool don't want us to, but there was a big price cut."
According to The Telegraph, Liverpool have rubbished these claims by reiterating that no bids were considered until this window, when the Merseyside outfit reluctantly agreed the transfer due to pressure from Coutinho and his camp.
The report adds that the Brazilian contributed £11.5m to the fee.