Although the Premier League's transfer window closed last week, European clubs have until September 2 to register new players.
That leaves open the possibility that Madrid could yet prise Pogba away from Manchester United in the coming weeks.
However, Madrid will officially end their interest in the French World Cup winner if they are able to sign Neymar from PSG.
Los Blancos are battling Barcelona for the signature of the Brazil forward, who is desperate to depart the Parc des Princes.
Madrid are confident of landing Neymar ahead of their rivals, which would virtually guarantee Pogba's presence at Old Trafford for the rest of 2019/20.
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