The 60-year-old was instantly offered the chance to take over the Premier League side but is reportedly reluctant to grab the opportunity.
Indeed, the Foxes recently sacked Nigel Pearson and weren't said to have had anyone lined up ahead of what was an impromptu decision based on an argument between the coach and the club's vice-chairman.
Ex-West Ham boss Allardyce was immediately installed as the favourite to take over at Leicester.
But the Mirror suggest ex-Celtic and current Bolton Wanderers boss Neil Lennon (who used to play for Leicester) is now in pole position to succeed Pearson, as Allardyce wants to take an extended break.
And the reason behind his motives are reportedly the stress he encountered while receiving abuse from the Hammers faithful last term.
The human side?
However justified West Ham supporter criticism of Allardyce may have been, the Leicester reports show the human side of football management.
The 60-year-old would no doubt have been offered a handsome wage to take over the Foxes but it appears simple rest could be the order of the day for Big Sam.