Philippe Coutinho is the world's third most expensive player
Barcelona will have to pay an extra 100 million euros (£89 million) on top of any transfer fee if they try to sign another Liverpool player before 2020.
BBC Sport understands the deal was struck as part of Brazil playmaker Philippe Coutinho's £142 million move to Barcelona in January.
Coutinho, 26, joined former Liverpool striker Luis Suarez at the Nou Camp.
According to The Times, the deal was brokered by Liverpool's sporting director Michael Edwards.
Suarez made the switch from Anfield to the Nou Camp in 2014 in a £75m transfer, joining former Liverpool midfielder Javier Mascherano, who moved 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.
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Source: bbc.com