The Mirror says the Portuguese club are huge admirers of Strachan, who masterminded a couple of Champions League victories over the Lisbon outfit during his time at Parkhead.
Strachan had a great start to his Celtic career and even this season took the club to their best run in Europe for decades, but it is still not enough to silence his critics.
And with Rangers favourites to win the SPL title a move to Portugal might suit all parties, with Benfica making inquiries behind the scenes.
Strachan has told friends he is unhappy with some aspects of the job and is described as 'low' by close pals in the game.