His last spell in English football ended under a cloud of controversy. He left Tottenham in 2023 after criticism of the players and of the club's culture.
Eighteenth is United's lowest position after 10 games of a season for 40 years. The side are in the relegation zone.
After a brilliant start and end to last season following a January arrival, results have collapsed this term. United have only three wins from 15 matches in all competitions.
A further appointment would leave the club with as many managerial changes as it made across the previous 68 years, dating back to Sir Matt Busby's appointment in 1945.
A reported buyout clause in Pochettino's contract is worth $10 million (£7.44 million). It is also understood to contain clauses that would allow him to leave for specific high-profile jobs.
Howe, 48, left Newcastle in the summer after an underwhelming 12th-placed finish. Newcastle would be due only a relatively small amount of compensation if he were tempted by the Old Trafford job.
Emery's chances of leaving Aston Villa look slimmer. Despite the loss of the spine of his team over the summer, his new-look side are finding their feet, and he is expected to sign a new contract.
A serial winner, his managerial credentials are not in doubt. What remains open is whether his fiery nature, and a history of falling out with clubs, would count against him.
Nagelsmann, still only 39, has seen his reputation take a hit, but he is still regarded as one of Europe's best coaches. Only Hansi Flick, at 88.9%, has a better Champions League win percentage as a Bayern Munich manager than Nagelsmann's 83.3%.