The Advertiser understands the Millers are in a three-way fight to sign the 34-year-old Coventry City man and a decision from him is expected by the end of the week.
Kelly has made 180 appearances for Coventry since joining them seven years ago.
A creative play maker, Kelly started his career in his native Scotland with Kilmarnock and played for Bristol City, Oldham and Leyton Orient before ex-Rotherham boss Mark Robins took him to Coventry and made him one of his main men.
Millers manager Steve Evans is already well on with filling the gaps left by the departure of 17 players after relegation from the Championship last season.
Striker Jonson Clarke-Harris, midfielder Shaun McWilliams, left-back Reece James and experienced defenders Joe Rafferty and Sean Raggett, who both won League One with Portsmouth last season, had already signed in before Burton Albion midfielder Joe Powell took the tally of new arrivals to six yesterday.
Evans said: “I have to credit the chairman and the board. When I had the opportunity to come back it was never about what my personal terms were. It was whether the chairman and the board were going to be delivering and he has always done that.
“He has always stood up and told me to go and build a squad and I feed back into the chairman and the board on a daily basis.”
Added Evans: “We’ve done some really good work so far but we have some fine tuning to do.
“It’s like we’ve bought a grand piano and it’s looking tremendous sitting in the far corner but you need to fine tune it.
“We’ll get into fine tuning territory after the weekend when we start really breaking down our squad.”
