The pair’s current contract ends at the end of the month but were both offered bumper new deals by the Millers in a bid to keep them at the club.
Both players explored their options and the possibility of joining other clubs, but Warne stayed in the game, refusing to implement a deadline, and it looks to have paid off.
Warne says he is confident of keeping “one or both” ahead of the club’s return to pre-season training on Thursday.
Warne told BBC Radio Sheffield: "In regards to Smudge (Smith) and Icky (Ihiekwe), I know they are well thought of at our football club. We have done everything we can with the chairman's support to try and keep them.
"I am pretty confident of keeping one or both, but I also could have gone down a different route and been criticised for it. I could have literally said to them, 'It is now or never, literally sign it or we part company.'
“But I have a real tight relationship with both players and understand their quandary.
"They are at an age where it is their last big contract, they want to see what is out there.
"I have always left the door open for them and always been honest and candid. I have spoken to them at least two or three times a week at least for the last four weeks and I have even sent them comedy video messages, when I have had a drink, begging them to stay!
“I think we have done everything we can and I am hopeful that both will stay, but I cannot guarantee it.”
The Millers boss expects to be busy between now and the end of the week, with several signings due to be completed.
He said: “We should have two wing-backs in by the end of the week, they should be joining in on training on Thursday, I would like to think we should have one or two strikers in by then, one or two centre-halves by then. We are in a really good position.”