Gakpo was strongly linked with Manchester United, but the Merseyside club have jumped to the head of the queue by making a formal offer to PSV.
The PSV star has been in fine form this season, netting nine goals and 12 assists in the Eredivisie.
He has also bagged three goals and three assists in five games in the Europa League.
The Netherlands international carried his superb form into the World Cup, where he scored three goals in five games.
Louis Van Gaal led the Dutch team to the quarter-finals, where they crashed out against Argentina after penalties.
Gakpo sparked the interest of multiple clubs, especially Man United. They pursued Gakpo last summer but switched their attention to Antony.
Leeds United came close to signing Gakpo on the final day of last summer’s transfer window, but things did not work out.
Gakpo will provide competition for Luis Diaz on the left side of Liverpool’s attack. The Colombian will be out of action for the next three months after undergoing surgery on a knee injury.
Liverpool have a strong relationship with Gakpo’s representatives, SEG. They represent Manchester City manager Pep Guardiola and Ten Hag.
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