Barcelona vice-president Jordi Mestre says his club were able to sign Philippe Coutinho this month because Liverpool finally lowered their demands.
The transfer fee is the second-highest ever, with ESPN FC sources and multiple reports saying it will reach £142 million (€160m), with Liverpool receiving £105m (€120m) up front and the rest in performance-related add-ons.
The Catalans had three bids rejected for the Brazil international in August but, at his official presentation to the media in the Camp Nou, the 25-year-old thanked Liverpool for "keeping their word."
Liverpool always denied claims in the Spanish press they had quoted €200m euros (£176m) to Barca for a summer transfer, but Mestre nevertheless insisted the Coutinho fee is much less than they could have paid previously.
"The interest of the club has always been to take Coutinho to Barcelona," Mestre said. "The difference is that there has been a substantial reduction in the cost of this transfer.
"There has been a very important reduction, even though we cannot publicly give the figures. We are not going to discuss the numbers. The important thing is we have the player here. If I reveal numbers I will be breaking our agreement with Liverpool."
However, The Telegraph, citing "Liverpool sources familiar with the negotiations," reported on Monday night that the club rejected Mestre's claim because no price was ever set in the summer.
Mestre also appeared to confirm reports the Brazil international had contributed £9m -- rising to £11.5m -- out of his own pocket to make the deal happen.
"Philippe, welcome. We know that you have made a personal and economic effort," he added. "In the last months we have dreamed of this moment, we wish you the best, which is the best for all."