The Saints can refuse United to talk to Strachan, as is their right under Premiership rules, but the report also states that Trevor Birch has spoken to Southampton chairman Rupert Lowe and with just over six months left on Strachan's contract, he may release him early.
Strachan will now be given permission to talk to Leeds to discuss terms and length of contract if he really wants a move back to Yorkshire.
Caretaker boss Eddie Gray was expected to be in charge of the team for the match against Bolton this Saturday, but all that may change this week.
Strachan captained Leeds to the Division Two title in 1990 and two years later, at the age of 35, led them to the Division One Championship in its last year before the inception of the Premiership.
Strachan still has a soft spot for The Whites and the new regime - which includes the wealthy sheikh Abdul Mubarrak Al-Khalifa - has money to spend on new players, making a return to Elland Road much more attractive.
Gordon Strachan returned to management with The Saints in October 2001 when he was asked to help Southampton escape a relegation battle after a disappointing start to the season saw them lose six of their first eight games. That sound familiar?