The one-time Barnsley frontman, 24, is on the radar of several clubs including Peterborough United and the Millers, who have both seen offers rebuffed.
The Millers are likely to maintain their interest in Jackson, who struck 16 times last season, but are currently in no rush to push through a deal.
Warne, who has completed his fourth summer signing after bringing in experienced defender Billy Jones, 31, on a two-year deal, said: “I have got four good strikers, but I would like another. Kayden Jackson is one who is on everyone’s list and I am not speaking disrespectfully to Accrington, as it has been well documented that lots of people have put bids in.
“But at the moment, the price tags on some players is too inflated. We will wait and see over the next couple of weeks when they (clubs) do not get what they want and teams start to look at different things.”
The Millers are in the market for several other players and are keen on bringing back former loan keeper Marek Rodak for a second loan spell at the club from Fulham, but are being forced to wait until a deal can be sanctioned with the Cottagers currently solely focusing on inward deals.
Rotherham are hoping for a decision as to whether Rodak – the club’s main goalkeeping target – can return by the end of next week or will switch to other targets, in all likelihood.
Warne said: “Realistically, I cannot have a goalkeeper coming in, potentially as a No 1 and not have at least a week’s training with the team (before the opening game).”
Another ex-loanee in Brighton midfielder Richie Towell is also on Warne’s list, with the Millers chief hoping to bring in two new central midfielders.
Nottingham Forest’s Ryan Yates is another player on the Millers’ radar. Contact has been made with Forest, but the player is currently ‘part of their plans’, according to Warne.
On new signing Jones, Warne said: “Most of the players who I have signed have been young, athletic types who we are trying to improve. But I am well aware of the difficulties in the Championship and we definitely needed some experience at the back as we rely on Woody (Richard Wood) quite a lot.
“Billy can also play in a few positions, which will help us and he can play as a sitting midfielder if I need him to and on both sides. I think it is a really good acquisition for us.”
Striker Jamie Proctor featured in a behind-closed-doors game yesterday, with loan defender Zac Vyner, currently sidelined with a groin issue, likely to be available for the home friendly with Cardiff City on Wednesday.
Darren Potter (Achilles) remains on the injury list and will be out until the New Year.
Young striker Jerry Yates has joined Carlisle United on loan until January.