Grayson stepped down in September after eight years in charge, with assistant head coach and former England bowler Chris Silverwood in temporary charge.
Silverwood is one of the five applicants who will be interviewed.
"It's mixture of people from overseas and the UK as well, it's a fair mix and I'm chuffed to bits with who's come forward," said Essex's Ronnie Irani.
"It's a big job. Essex is a big club, it's a huge name globally in the world of cricket," added the former Essex skipper, who is now the club's cricket committee chairman.
Essex finished third in Division Two of the County Championship in 2015, but have not featured in the top flight since their relegation in 2010.
"We've just got to take our time and make sure we've got the right person with the right attitude who's got the county at heart," said Irani, who captained the club to the Division Two title in 2002.
"We need a coach who's going to fully commit and give as much energy as possible because that'll rub off on the players. We'll be successful and we'll win things if we get that recipe right."
Essex have compiled a shortlist of five candidates to replace Paul Grayson as the county's new head coach.