If other results go the club's way, Mauricio Pochettino's charges could even find themselves second - a scenario that illustrates the club's remarkable start to the campaign.
With just one defeat to its name this season - a record shared only by Everton and table-topping Arsenal - Southampton has established itself as outside contender for a European berth.
The south coast club had to settle for a point last time out, Jay Rodriguez's goal earning a 1-1 draw at the Britannia Stadium after Stoke City goalkeeper Asmir Begovic had opened the scoring from almost 100 yards 13 seconds into the game.
Rodriguez has since gained a first call-up to the England squad and will link up with Southampton teammates Adam Lallana and Rickie Lambert for friendlies against Chile and Germany.
Hull City, meanwhile, is currently the highest-placed of the promoted sides, with a 1-0 victory over nine-man Sunderland last weekend lifting the club to 10th.
Fixtures between these sides have not been short of goals in recent years, the last five meetings producing a total of 20.
Southampton has had the better of the tie historically and won both encounters when the sides last shared a division - the Championship - back in 2011-12.
Hull boss Steve Bruce is full of praise for this season's surprise package in the Premier League.
"I have to say, Southampton have been a breath of fresh air when you look at the young players they've got," he said. "Only a few years ago the club was in administration, but fair play to them all - they've done a wonderful job.
"To get 19 points from 10 games is a wonderful achievement and it's as hard a game as we'll have. This will be another big, big test for us."
The home side could welcome back record signing Dani Osvaldo, who has been absent for three matches with a nerve problem, but Guly Do Prado (knee) remains sidelined.
Hull striker Sone Aluko was ruled out for eight to 10 weeks on Thursday after suffering an Achilles tear in the warmup ahead of the clash with Sunderland.
The 24-year-old missed the second half of last season with a similar injury and a scan has indicated he is set for another lengthy spell on the sidelines.
James Chester (hamstring) and Allan McGregor (thigh) are also set to miss out for Hull.
In other injury news, referee Howard Webb has had to pull out of the tie and will be replaced by Phil Dowd.