Southampton have surprised many with a superb start to the campaign, rising to second in the table after nine matches.
A stunning 8-0 win over Sunderland was followed by a battling 1-0 victory against Stoke City last Saturday, while Wednesday's League Cup triumph over Mark Hughes' men secured a quarter-final spot.
With nine wins from the last 10 matches in all competitions, Koeman's men are in excellent form, but the trip to the KC Stadium represents their third fixture in eight days.
"The lads are showing great ambition," the Dutchman said following the midweek win.
"They will be tired, but if you're winning you're not so tired."
Koeman made four changes for the Britannia Stadium success, with Shane Long taking advantage of his inclusion to net his first goal for the club since making the switch from Hull in August.
The Republic of Ireland international will now set his sights on breaking his Premier League duck for his new side, with his maiden strike offering a timely boost ahead of a return to his former employers.
"It's a purely selfish thing getting that first goal under your belt," he said. "I'm obviously delighted to get it.
"It wasn't getting me down too much, but it's always easier when the team is doing so well."
Hull also have cause for optimism after putting together a three-game unbeaten run in the league, including draws at Arsenal and Liverpool.
That run has left Steve Bruce's side 10th in the table and centre-back Alex Bruce noted the huge upturn in the club's fortunes over the past two seasons.
"It is unbelievable to think how far we have come," he told The Hull Daily Mail. "The supporters must agree with that. Things have changed so much since I first came here."
Hull, who denied an approach was made by Fulham to talk to their manager before Kit Symons was appointed at Craven Cottage on Wednesday, will be without Gaston Ramirez, who is ineligible to play against his parent club, while out-of-favour forward Tom Ince joined Nottingham Forest on loan in the week.
Michael Dawson (ankle), Nikica Jelavic (knee), Allan McGregor (shoulder) and Steve Harper (arm) also remain out.
Southampton have no new injury concerns, meaning Jay Rodriguez and James Ward-Prowse (both knee) are the only two definite absentees.
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