Barcelona must pay 100m euros (£89m) on top of a transfer fee if they try to sign a Liverpool player before 2020.
BBC Sport understands the deal was struck as part of Brazil playmaker Philippe Coutinho's £142m move to Barcelona in January.
Coutinho, 26, joined former Liverpool striker Luis Suarez at the Nou Camp after he moved in 2014 for £75m.
According to The Times, the extra charge was brokered by Liverpool's sporting director Michael Edwards.
Argentina midfielder Javier Mascherano also made the move from Liverpool to Barcelona, doing so in 2010 for £17.25m.
Barcelona originally wanted to sign Coutinho in August 2017 following the departure of Neymar to Paris St-Germain but were forced to wait until January after Liverpool initially refused to let the Brazilian leave.
Coutinho has five goals in all competitions for Barcelona this season.