South African sides Cheetahs and Southern Kings are set to join the league for the 2017-18 season after losing their Super Rugby status.
The expanded Pro12 is likely to split into two groups, but games between local rivals will remain even if they play in different conferences.
Derbies attract the competition's biggest crowds and are set to be part of a 21-match regular season.
The two South African franchises will join four Irish provinces, four Welsh regions, two Scottish and two Italian teams who play in the Pro12.
The four Welsh regions and Irish provinces currently play six derby matches in the regular season, with the Scots and Italians playing two each.
A new Pro14 league is due to kick off in the first week of September and will comprise two conferences of seven teams. Each conference will have one Scottish side, one South African side, one Italian side and two each from Wales and Ireland.
The current preference is for two conferences of seven teams playing each other home and away. Within this format, the teams would also play one game against all the sides from the other conference, which would deliver 19 fixtures.
Additionally, each club would also play home and away derby fixtures as well, providing a total of 21 league games.
That will require Edinburgh and Glasgow, Zebre and Treviso and the Kings and Cheetahs facing each other three times in the regular season.
However, other formats are also being discussed.
The Welsh showcase Judgement Day - which sees two derbies played back-to-back at Cardiff's Principality Stadium - is set to continue.
Another question about an expanded Pro12 tournament is how it would affect European qualification.
At the moment the top seven sides regardless of nationality qualify for the Champions Cup with the further five in the Challenge Cup.
It is unclear whether South Africans would be allowed to compete in Europe's premier tournament, and how qualification would be decided  from a two conference system.
European Professional Club Rugby (EPCR), which organises both tournaments, says it has had no formal discussions about the South African sides joining.
An EPCR statement said: "At the present time, neither the EPCR executive committee nor board has been involved in formal discussions concerning the implications of clubs from non-European countries entering into one of the three European professional leagues.
"Should such a situation arise, EPCR would require the necessary information from its stakeholders in the league concerned before making a decision regarding access to its competitions in keeping with the Heads of Agreement."
Celtic Rugby have confirmed they have been talking to the South African sides about joining an expanded Pro12.
A statement read: "Celtic Rugby can confirm advanced and positive discussions are taking place with the South African Rugby Union regarding the introduction of two teams into an expanded Guinness PRO12 Championship.
"Given the proximity of the 2017/18 season start, a final decision on this potential expansion will be confirmed as soon as practical."
Lucrative domestic derby matches would be protected in an expanded Pro12.