The Examiner says he has emerged as a potential front-runner for the England under-21 job.
Although Aidy Boothroyd is still technically in charge, it is widely expected that he will depart his role as Young Lions' boss.
Boothroyd's side had a disastrous European Championship that culminated in elimination despite a 2-1 win over Croatia. They lost their opening two games to Switzerland and Portugal.
The 50-year-old has been in charge since 2016 but thoughts are already turning towards his potential successor.
Lester, who represented the Blades during his playing days, has been in his current role at Shirecliffe since 2019.