The centre-back was recalled by the Millers last week midway through his season-oan loan spell at the DW.
It was expected a deal would be arranged to see Tilt - who has joined Latics on loan in each of the last three transfer windows - become a 'Tic on a full-time basis.
So far, though, an agreement has proved elusive.
And while Tilt will almost certainly become a Latics player before the end of the month, Warne has begun to discuss the possibility of him remaining with the Millers.
"Earlier in the week, I was pretty confident that something definitive would have happened by now, whether that be Wigan or another club purchasing him," he said.
"I thought it would have been done by now, but it hasn't been done by now.
"I now regard him as my player until I'm told differently, and I'll get him ready with the rest of the squad for Saturday.
"It hasn't materialised the way I anticipated - keeping him on board.
"It's why you're called a football manager - you have to manage people.
"That part of the job is probably greater than the tactics and getting players to run through brick walls for you.
"I will talk to Curtis. I do talk to Curtis. I've been on the phone to him twice a day at least for the last five days.
"I explain it to him as honestly as I can. I don't make every decision at the club, quite obviously.
"I guess the manager of Tottenham sat down with Harry Kane when Kane's move to Manchester City didn't happen. That's how football is sometimes.
"If Curtis stays, he knows I rate him as a player. We'll do everything we can to help him compete with the lads who are doing well.
"I haven't got a magic wand that I can wave and he's like: 'Yeah, I feel amazing, gaffer.'
"I know he's not going to be fully on board for a bit, but he's a professional and I expect him, as a professional athlete, to knuckle down and join in with the group.
"He'll soon be incorporated and welcomed back into the group.
"In a couple of weeks' time, it might be a distant memory for him."
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