The departure of last season’s top goalscorer Michael Smith, allied with stepping up a division to the Championship, has put the spotlight on the attacking position as an area the Rotherham United need to strengthen.
Conor Washington and Tom Eaves have been signed this summer but Warne has been frustrated elsewhere in his attempts to bring in an extra front man.
Chiedozie Ogbene played in that role in the season-opener against Swansea City and scored a goal in an impressive performance.
Eaves should return to training in the next 10 days, and Warne presently appears to be content with his options.
“At this moment in time, we’ve got Conor, Chieo and Georgie (Kelly) fit, with Tom Eaves coming back.
“We could still do with another one and we are trying to do that. But they need to tick all the boxes for us, there’s no point signing someone who isn’t better than what we already have.
“If it doesn’t come off and we go into the season with what we’ve got that’s absolutely fine. As I said, we need to get one to tick all the boxes, which is what we’re trying to do.”
Meanwhile, the game has been placed in doubt after it was confirmed a pitch inspection will take place on Saturday evening.
The Sky Blues are due to stage their first home match of the new season against the Millers on Sunday afternoon.
But the playing surface has been affected by the Commonwealth Games rugby sevens being staged there.
A statement read: “Coventry can confirm that there will be a pitch inspection at the Coventry Building Society Arena at 6pm on Saturday, ahead of our home game against Rotherham.
“Concerns have been raised regarding the condition of the pitch at the Arena and there will be an inspection by a senior referee.
“We will keep supporters updated.”
Defender Lee Peltier and midfielder Scott High, two signings made last week, could feature if the game goes ahead on Sunday after sitting out the draw with Swansea.
Warne said: “They’d only just arrived and hadn’t done a lot of work with us. I always try to run a fair ship and pick the best squad I can.
“If I feel that they are the right players to player they will be picked and they’ve both trained really well this week.
“We had a game amongst ourselves between the youth team on Wednesday, there we some really good performances and we’ve got a good squad to pick from.”
Coventry are managed by former Millers boss Mark Robins, a man who brought Warne back to Rotherham United more than a decade ago.
““He’s had an unbelievable career in management, “ said Warne. “He’s built the team up and has built a clear identity of how he wants to play.
“I think his teams have really overachieved over the years which is testament to them and him.
“Last season, it looked as if they were going to get in the play-offs, which would have been amazing, so we know it’ll be a tough test. I expect them to have another good year.”