The club's reward for beating high-fliers Burnley 4-3 at St Mary's yesterday is a visit from struggling Yeovil Town.
The Glovers defeated League 1 promotion hopefuls Leyton Orient 4-0 at Huish Park yesterday with ex-Bournemouth striker James Hayter scoring twice.
Saints played Yeovil four times in their two League 1 seasons a few years ago, winning three of them.
Yeovil held Saints 1-1 at Huish Park in September 2010, but Saints won 3-0 at St Mary's later in the season with Barnard (2) and Alex Chamberlain on target.
Yeovil have two ex-Saints in their ranks.
Striker Sam Hoskins was not in the squad yesterday, though he did come on as a sub in their 5-1 loss at Huddersfield on New Year's Day, while defender Danny Seaborne is on loan at Coventry.
Fourth round draw: Sunderland or Carlisle v Kidderminster or Peterborough, Bolton v Cardiff, Southampton v Yeovil, Huddersfield v Charlton or Oxford, Port Vale or Plymouth v Brighton, Nottingham Forest v Ipswich or Preston, Southend v Hull, Rochdale v Macclesfield or Sheffield Wednesday, Arsenal v Coventry, Stevenage v Everton, Wigan or MK Dons v Crystal Palace, Derby or Chelsea v Stoke, Blackburn or Manchester City v Bristol City or Watford, Bournemouth or Burton v Liverpool or Oldham, Birmingham, Bristol Rovers or Crawley v Manchester United or Swansea, Sheffield United v Norwich or Fulham. Ties to be played on the weekend of January 25 and 26.