The 33-year-old, who began his career as head of football development at Falkirk, has been identified by the Ibrox club as their number one candidate for what they regard as a key position in a revamped management set-up.
Rangers had hoped to be in a position to make an announcement on the position no later than yesterday but have agreed to give Wilson more time to reach a decision.
Southampton are keen to retain the services of Wilson, who joined them in March 2015 and has impressed with his contribution to their consistently successful player recruitment network.
Wilson has worked in English football since 2011 when he left Falkirk to join Watford as football business director. He moved on to Huddersfield Town just over a year later as head of football operations.
Rangers still hope to have both Wilson and a new manager in place by the middle of next week. Pedro Caixinha, the Portuguese coach currently at Al-Gharafa in Qatar, remains their preferred choice after a lengthy process which also saw former Birmingham City manager Gary Rowett and ex-Ibrox boss Alex McLeish interviewed.
Caixinha is understood to be returning to Europe this weekend as the Qatari League enters a three-week break. Rangers are keen to conclude a deal before the Old Firm game at Celtic Park next weekend. Graeme Murty remains as caretaker manager for today’s Scottish Cup quarter-final at Ibrox.
It will be his fifth game in charge since Mark Warburton’s contentious departure on 10 February when Rangers stated he had resigned, along with assistant David Weir and head of recruitment Frank McParland. That was denied by Warburton, amid reports the trio had been targeted for jobs at Nottingham Forest.
That link was strengthened last night when Forest confirmed the appointment of McParland as director of football amid fresh speculation Warburton will follow him to the City Ground as manager. Gary Brazil has been in interim charge since Frenchman Philippe Montanier was sacked in January.
Warburton, Weir and McParland have enlisted the help of the League Managers’ Association in England to pursue a legal settlement with Rangers over their exit from the club.