The 23-year-old, who can also play in defence, had been linked with a move to Easter Road and Motherwell, but according to reports in The Sun, the English League One outfit will win the race for his signature.
They claim that the Millers have already had two bids rejected, but will return with a third successful offer in the next 48 hours to seal a five-figure deal.
Odoffin joined Hamilton from Livingston last summer and was one of their stand-out performers despite Accies suffering relegation to the Championship.
The former Northampton Town player has missed much of pre-season due to contracting Covid-19, but now it looks like he will be plying his trade in Yorkshire next season for Paul Warne’s team.
Rotherham have also been credited with an interest in St Johnstone right-back Shaun Rooney.