Mana Otai's contract was not renewed after the Kingdom's disappointing finish at the Rugby World Cup, where they beat Namibia but lost to Georgia, Argentina and New Zealand.
The Interim Chair of the Tonga Rugby Union, Fe'ao Vunipola, said finding a replacement was complicated by staffing changes and financial concerns at the Union.
He said, after successful talks with the Government and World Rugby earlier this month, they intended to interview shortlisted candidates as soon as possible.
"We are looking to confirm the appointment by the end of the month so the coach will start...we wish we had done it months ago like Samoa and Fiji but our hands were tied, as you know, so this is the best we can do now is to appoint the coach ASAP and let him do his job."
Tonga begin their 2019 World Cup qualifying campaign with matches against rivals Fiji and Samoa in the new Pacific Tri Series.
All three countries will also play a one-off test against Georgia, with Tonga's to be held in Suva because Teufaiva National Stadium is being upgraded.