The Saints have been confident about getting a deal done to sign the winger from PSV going into the final day of the window, despite competition for his signature.
Leeds have also been interested in him, but Southampton have been getting increasingly confident about signing the winger.
And it has been claimed that a deal is now in place between Southampton, PSV and the player for the transfer.
The Saints have agreed on a fee with the Dutch giants for the signature of the 23-year-old winger.
Southampton have also thrashed out personal terms on a contract with the player and his representatives.
The deal is now hinging on whether PSV want to act on the agreement they have with Southampton and sell Gakpo.
The winger is currently in action in PSV’s Eredivisie clash against FC Volendam at the Philips Stadion this evening.
Southampton will hope to have everything sorted out in time to sign Gakpo before the window closes on Thursday night.
It remains to be seen if Leeds might yet match Southampton’s offer.