Robbie Neilson s men have already topped the group and qualified for the knockout stages. But they will be looking to make it four wins from four to give themselves the best chance of finishing as one of the three best group winners to secure a seeded spot.
The country's European entrants – Rangers, Celtic, Aberdeen, Hibs, and St Johnstone – enter at the second round stage.
Hearts have been professional in their work so far, seeing off Peterhead, Cove Rangers and Stirling Albion without losing a goal.
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How the Hearts players rated in the draw against Hibs
How the Hibs players rated in the derby draw with Hearts
Inverness are familiar foes in the League Cup group stage. This is the third time they have faced each other in the last four seasons.
The Highlanders, under new boss Billy Dodds, have picked up four points, winning, losing and drawing a game so far. Hearts legend John Robertson, who is now director of football at ICT, was in attendance to see his former club play Stirling on Tuesday.
Team news: John Souttar got a kick late on against Stirling but is fine, while Armand Gnaduillet returned to the team making a substitute appearance. Robbie Neilson confirmed the club are managing Jamie Walker’s fitness and that back-up right-back Cammy Logan has a back issue but has been able to do some running as he gets back to full fitness. The manager revealed he doesn't expect to overhaul the team for the ICT game despite the group having been won.
Possible XI: Gordon; Popescu, Halkett, Cochrane; Smith, Pollock, Halliday, Mackay-Steven; Walker; Boyce, Gnanduillet.
What the manager said: “It’s good to get the three points, that’s us on nine now so that is us qualified for the next stage, which was the most important thing for us. We will make some changes for Sunday but nothing major, we want to keep some momentum going and we want to make it four out of four wins.”
Match details: Sunday, July 25. Kick-off 5.15pm Tynecastle Park, Edinburgh.
How to watch: The match is live on Premier Sports 1 with build-up starting at 5pm following the conclusion of the Partick Thistle v St Mirren match. The game will be available to view on HeartsTV but only to international subscribers with audio coverage for UK subscribers.
Last meeting: You only have to go back to April for the last time these clubs met. It was a special day for Hearts as it was trophy presentation day at Tynecastle Park having wrapped up the Championship title. The home side ran out comfortable 3-0 winners with a confident performance, the goals being scored by Aaron McEneff and Gary Mackay-Steven who grabbed a brace.
Key stat: Hearts are 12 games unbeaten against Inverness CT in all competitions. Neilson’s men are currently on a run of eight games without defeat and without conceding.
Referee: Nick Walsh – The referee took charge of just three Championship matches last season, two of which involved Hearts. One was the meeting with Inverness in the Highlands, a game which finished 1-1. The other was the 3-1 home win over Arbroath where he awarded Hearts a penalty.
Match odds: Hearts 40/85 Draw 15/4 Inverness CT 5/1