The Mail Online reports that the two clubs are in advanced talks and hope to complete a deal next week.
Since his appointment at the club, Ronald Koeman has made it his mission to focus on the long-term future of the club by bringing in a host of talented young players for the academy system.
Players such as Ademola Lookman have played a prominent role in the first-team squad with Koeman putting his faith in the club’s young stars.
Gibson, a left-sided defender, who can also feature in the centre of defence, is highly rated at Newcastle, who would have been desperate to keep hold of him.
Head of recruitment Steve Walsh, who joined from Leicester last summer has been working on the deal with the recently promoted side and has been responsible for a number of transfers at the club.