The former England manager took over in September 2017 and has maintained the club's Premier League status ever since.
Hodgson will end his spell in charge of his boyhood club following the final game of the campaign away to former side Liverpool on May 23.
Here, the PA news agency takes a look at the possible replacements for the 73-year-old.
Heavily linked with the vacant Celtic job, Howe could stay closer to home if he was to move to Crystal Palace after being out of work since he left Bournemouth in August. The 43-year-old remains one of the brightest young managers in the country despite the Cherries' relegation last term. He guided the south coast club through the divisions into the top flight playing an attractive brand of football and boasts a wealth of experience.
Eagles chairman Steve Parish is said to be a long-term admirer of the Burnley boss, who was linked with a switch to Selhurst Park in 2017. With the Kettering-born manager not afraid to speak out about the difficulty of working with a small budget at Turf Moor, a move down to London with more money to spend could be tempting. Dyche has enjoyed a hugely successful nine-year spell with the Clarets, but a change may be right for all parties.
The former England midfielder worked under Hodgson at international level and would be a high-profile appointment. He was sacked by Chelsea in January following 18 months in the hotseat at Stamford Bridge and gained recognition for his work with the club's bright young talent. Crystal Palace have recently redeveloped their academy set-up and could opt for Lampard in the hope he could bring through more youth-team players, but the ex-Derby manager is understand not to be in a rush for another role and his wife gave birth in March.
Out of work since he left Sheffield United in March, Wilder revealed he was enjoying a period of reflection in April but would be a contender for the role at Selhurst Park. He impressed during the Blades' return to the Premier League last season with an expansive style and gained numerous plaudits for his overall work with the Yorkshire club. Playing spells at Charlton and Brighton are unlikely to count against the 53-year-old.
The Champions League winner is out of work after he departed Chinese Super League outfit Dalian Professional in January. After success spells with Liverpool, Chelsea and Newcastle in the Premier League, Benitez would fit the bill in SE25 of a manager who could attempt to take the club to the next level. Experience at both ends of the table – keeping the Magpies in the division, while regularly qualifying for Europe at Anfield – would be a big tick against his name on the shortlist.