The Young Lions crashed out at the group stage of the U21 European Championship this week after losing two out of their three matches in the competition.
Their failure to progress has piled pressure on Boothroyd, who has held the role since 2016 – so much so that he must now reapply for his role with the national setup if he wishes to keep his job, as per the Daily Mail.
The FA will also consider other candidates, and it is understood that Lester is in the running to replace the 50-year-old, as per TEAMtalk.
For his part, the Blades academy boss has been at Bramall Lane since 2019, after previously managing Nottingham Forest’s U23s and Chesterfield Town.
Some of the other names in the running include Jody Morris, Steve Cooper, Jason Euell.
Elsewhere, KV Oostende boss Alexander Blessin has emerged as a strong contender for United’s managerial vacancy, according to the Daily Mail.
The national title report that the Blades have already held extensive talks with the German, who has impressed during his current stint in Belgium.
A former RB Leipzig youth coach, the 47-year-old has led Oostende to fourth in the table in the Belgian top flight, and has averaged 1.58 points per game in his 33 matches to date.
Chris Wilder averaged 1.59 PPG during his entire five-year spell at Bramall Lane.
Another meeting has reportedly been set up to discuss Blessin’s candidacy further.
We’ve gathered up the rest of today's Premier League speculation below...