First-team coaches Ryan Mason and Chris Powell has been placed in charge on a caretaker basis until the end of the season, but who is in contention for the job permanently?
The RB Leipzig boss is the bookies' favourite and is thought to be well regarded at Tottenham.
Nagelsmann, 33, is one of the hottest managerial prospects in Europe having taken the Leipzig to the Champions League semi-finals last season. They are currently second behind Bayern Munich in the Bundesliga.
Nagelsmann has previously spoken about wanting to manage in the Premier League but Spurs would face competition from Bayern, who are tracking him after Hansi Flick announced he will leave the club at the end of this season.
The former Juventus manager has been biding his time over a return to management since leaving the Serie A giants in 2019 after winning five straight Italian titles and reaching two Champions League finals.
Allegri, whose Juve side knocked Tottenham out of the Champions League in 2018, fits the mould of a high-calibre manager with experience of delivering silverware.
The 53-year-old is keen on a Premier League job and has held talks with Arsenal in the past, while being tentatively approached to replace Frank Lampard at Chelsea earlier this year. He has also been learning English.
The Leicester manager will surely be high in Levy’s thinking after his work at the King Power.
But Rodgers, who led the Foxes to their first FA Cup final since 1969 on Sunday, will be difficult to prise away from Champions League chasing Leicester and his contract there runs until 2025.
The former Liverpool boss is keen on attacking football and developing younger players, which will appeal to Levy.
The Brighton manager has enjoyed a remarkable rise in recent years. After leading Ostersunds from the fourth tier of Swedish football into the Europa League, where they beat Arsenal at Emirates Stadium, Potter moved to Swansea City before taking over at Brighton and has been hailed as the brightest English manager by Pep Guardiola.
Potter prefers a possession-based, attractive style of football which would be a soothing change for Spurs fans who had grown frustrated watching Mourinho's football.
The Lille manager is not a fan of Mourinho. Galtier was left angered after Mourinho nabbed two of his coaches - Joao Sacramento and Nuno Santos - after taking the Spurs job in 2019, so there would be a fine element of karma to the Frenchman succeeding Mourinho.
Despite selling key players season after season, Galtier has turned Lille into title contenders in France. His side are currently a point clear of PSG, who have won the title in seven of the last eight seasons.