The region's chief operating officer says the claims of head coach Sean Holley and forwards coach Jonathan Humphreys will also be assessed.
New Zealander Hore, a former Wales fitness coach, said: "We definitely will be looking at both scenarios."
Johnson will become Scotland boss Andy Robinson's senior assistant coach.
Hore said: "We've been talking for a long period of time about where to go from here, that kind of thing.
"What we want to do now is sit down and look at the blueprint.
"We started this exercise four years ago to bring him [Johnson] in to help develop those coaches and that coaching staff and put those systems in place.
Are we happy with where we're at?
"And we've just got to review that now and make a decision on whether we bring somebody else in, that maybe the process needs to be finished.
"Or, are we happy with where we're at and go with from within, as we said?
"And then it's who, from within, is going to head that up?"
Hore admits the festive period has made it difficult for the Osprey's power brokers, such as joint managing directors Roger Blyth and Mike Cuddy, to meet to discuss the issue.
"With some directors being away, obviously with the festive period and that, we just haven't had a chance to sit down because it [the news about Johnson leaving] came out a little bit earlier than we expected," Hore added.
"So yeah, we've got a bit of work to do yet."
The Ospreys stopped a run of three defeats with a 17-12 win over Welsh rivals Cardiff Blues on New Year's Day at the Liberty Stadium.

Reports on Tuesday suggested the 28-year-old's representatives are set for talks with the English side.
"There are no direct offers," the source told BBC Sport.
"Only by meeting the release clause of 94,376,000 euros will the player leave Napoli. Otherwise Higuain will stay for the remaining two years of his deal."
Gareth Bale's £85m move from Tottenham to Real Madrid in 2013 is the most expensive transfer in football history, surpassing the £80m Real paid Manchester United for Cristiano Ronaldo in 2009.
In 2013, then Real Madrid forward Higuain agreed personal terms with Arsenal, but joined Napoli after the Gunners failed to make an offer.
Last season, Higuain won the Capocannoniere - Serie A's golden boot - after scoring a league record 36 goals as Napoli finished runners-up to Juventus.
Meanwhile, Napoli have not received any offers for 25-year-old Senegal centre-back Kalidou Koulibaly, who has been linked with Everton and Chelsea.

It will close to all traffic at 20:00 GMT and reopen 48 hours later, each weekend until 19 December.
During the works, about 50,000 tonnes of material will be laid on the 2.9km (1.8 mile) runway.
Traditionally, airports close for up to 14 days to carry out such work.
Airport bosses said completing the refurbishment over several weekends rather than all at once was the "best way to avoid major disruption".
The closures were agreed following two years of discussions with retailers and airlines, airport management added.
"Some of our retail partners are refurbishing their shops which they wouldn't be able to do when the airport is open," said Jack Kelly from EMA.
"We've made sure flights can come in ahead of the closure and more flights can go out after it, so we are limiting the amount of disruption."
The runway was last refurbished in 1999 and has a lifespan between 12 to 17 years.
Engineers will also be replacing 1,200 lights around the runway with LEDs.
The runway will be divided up into seven sections, with one chunk being repaired and sealed off each weekend.
Andrew Hore says the Ospreys will consider finding a successor for director of coaching Scott Johnson, who leaves for Scotland in June.
[NEXT_CONCEPT]
Arsenal must pay Napoli 94m euros (£80m) to sign Argentina striker Gonzalo Higuain, according to a source close to the Italian club.
[NEXT_CONCEPT]
East Midlands Airport (EMA) will shut later for the first of seven consecutive weekends to resurface the runway - a first for a UK airport, bosses have said.