Manchester United ended their interest in the Dutchman after they agreed to spend €100m to snare Antony away from Ajax earlier this week.
The winger could still end up in the Premier League before the transfer window closes on Thursday night, though Everton are not currently in the chase.
Southampton failed with a £21m bid for the winger recently, with PSV Eindhoven holding out for a deal worth £25m.
And it has been claimed that the Saints are still carrying out work to sign the attacker from PSV going into the final day of the window.
Ralph Hasenhuttl likes the winger and is pushing the south coast club to work out a deal with the Dutch giants.
Gakpo is keen on a move to the Premier League and is waiting for developments to unfold over the next few hours.
Leeds also have an interest in the Dutchman but currently, Southampton are the ones who are putting in the legwork to pull off a late move for him, and it remains to be seen if the Whites can nudge ahead in the chase.
