The Danish national coached the PNG Kapuls for 18 months, a period highlighted by a runners-up finish in the 2016 OFC Nations Cup, where they lost the final on penalties against New Zealand.
Serritslev left PNG three months before the end of his contract, after the PNGFA failed to pay him for the final year of his tenure, and is currently based in Armenia.
The 72-year-old, who has also had spells in charge of the Denmark and Armenian Under-21 sides, is set to replace former Fiji head coach Christophe Gamel who resigned in August last year.
Fiji Football Association chief executive Mohammed Yusuf said the appointment is not yet confirmed Flemming Serritslev but is set to arrive in the country this weekend to iron out the final details.
"We have interviewed and had a Skype meeting with the preferred candidate and we are happy that we have almost reached an agreement," he said.
"In the meantime we agreed that he comes over to Fiji and have four or five days, he moves around the country, looks at our culture and our football.
"And then finally at the end of the week, next week, when we settle we are ready to sign the contract and we will also sign a press conference with the President in the west and we will then announce the official signing and appointment."
Mohammed Yusuf says Fiji FA does have a Plan B if Flemming Serritslev opts not to accept the position.
If he does his first major assignment will be the OFC Nations Cup in New Zealand in June.