Portsmouth's board will interview the final two candidates from their seven-man shortlist on Thursday as they close in on naming a new manager.
The League Two club sacked previous boss Guy Whittingham on 27 November.
Oxford manager Chris Wilder, ex-Crawley boss Richie Barker and Exeter's Paul Tisdale have already been interviewed.
Pompey chief executive Mark Catlin told BBC Sport they hoped to make a decision by Friday and announce the name of the new manager on Monday.
He said the board had been "very impressed with the high standard of candidates already".
After Thursday's final interviews in Newbury, the board will then choose a preferred candidate, with the aim of agreeing personal terms over the weekend.
Wilder was interviewed on Tuesday after being granted permission to speak to Portsmouth, but will take charge of Oxford in Thursday's FA Cup first-round replay at Gateshead.
Former Crawley boss Barker remains the bookmakers' favourite, with Exeter manager Tisdale also among the front-runners having been interviewed on Tuesday.
The Grecians released a club statement on Thursday confirming they had allowed the Football League's longest-serving manager to speak to Pompey.
"Exeter City Football Club prides itself on not standing in the way of staff, players and management when opportunities arise away from the club," the statement read.
Meanwhile, caretaker manager Andy Awford has accused the Pompey players of being intimidated by playing at Fratton Park.
They trailed 1-0 to Wycombe on Wednesday before improving in the second half and eventually drawing 2-2.
"The first half was not good enough and it should not need me to go in and tell them that at half time," Awford told BBC Radio Solent.
"What was said will remain private, but it was not good enough. Second half I cannot fault them.
"I don't get how it can be so different in the first half. They were like rabbits in the headlights. They looked scared to play out there.
"It is an intimidating place to play for home players but they have to get used to it because they play for Portsmouth and that is not going to change."