It's not on the Saints official club website but Derby County have put up the details on theirs read of for the information.
Derby County will travel to St Mary’s Stadium to take on Premier League side Southampton in the Emirates FA Cup Third Round replay on Wednesday 16th January (7:45pm kick off).
Ticket prices will be as follows for Derby fans so I would assume that they will be the same for Saints supporters.
Adults (Season Ticket Holders): £10
Adults (Non-Season Ticket Holders): £12
Seniors (65+): £8
Under 22s (18-21): £8
Under 18s (11-17)*: £5
Under 11s (2-10)*: £5
Apparently the game will be broadcast live by the BBC.
UPDATE.
Info confirmed by Saints for tickets is as follows
On sale dates:
Season Ticket Holders - Wednesday 9th January 9am until Thursday 10 January 2pm
Members - Thursday 10th January 3pm
General Sale - Friday 11th January 9am
Prices:
Adults: £12 (£10 to Season Ticket Holders during Season Ticket Holder Window only)
Members: £12
Over 65/Under 21: £8
Under 18: £5
Blocks 12 - 26 (Chapel End) will NOT be open for this fixture. Season Ticket Holders seated in these areas will not be able to purchase their regular match seat(s). Instead, those supporters effected will be able to purchase a seat that is not currently held by another 2018/19 Season Ticket Holder in a different area of the stadium from Wednesday 9 January at 9am. Family enclosure for this match is made up of Blocks 11 and 27 - though it is the same prices in all available areas of the ground. Due to this being a replay, ticket buying windows are shorter than normal.