The sum relates to a £15m deal for BetVictor to sponsor the English Premier League team’s training kit.
Winlink claims Liverpool owes the company £1.125m because one of its senior executives introduced club officials to its BetVictor contacts in 2013.
However, Liverpool says Rafaella Valentino, its head of global partnership sales, personally negotiated the deal with Betvictor CEO Andreas Meinrad.
At a remote High Court trial, Winlink barrister Andrew Sutcliffe QC said the company "spent significant time and effort in building the relationship between Liverpool and BetVictor."
According to Sutcliffe, Winlink "accepted that it played no role in the negotiation of the 2016 agreement itself" but was "simply providing an introduction service."
By not paying commission for these services, Sutcliffe said "Liverpool has not kept its side of the bargain."
Liverpool's barrister, Robert Anderson QC, argued Winlink's introductions "had nothing to do with the execution of the £15 million training kit deal."
He said Winlink is not entitled to commission "because the introductions were made two-and-a-half years before the 2016 deal."
