Evans, who has a family home in Peterborough, has been the overwhelming favourite with the bookmakers following Dave Robertson's sacking last week, but MacAnthony looks to have ruled out a move for the Scot on Twitter.
In a Q + A session on the social media site, the Posh chief replied to a Millers fan who asked whether there was any interest in Evans with "absolutely not".
It looks to bring an end to a week of uncertainty over Evans' future in South Yorkshire, with the Millers boss maintaining a silence over the links - the second time in six months he has resisted the opportunity to bury the speculation.
Despite performing press duties for the club's in-house media channel, Evans sent assistant Paul Raynor to face the local media immediately after as he was tied up in an "internal meeting".
Raynor, who has been Evans' assistant for over 10 years, was not aware of any approach by Posh, but understands where the speculation comes from.
It's a busy period, we have got two games away, we are staying away so there is lots to organise before we go. There's no hidden agenda," Raynor said of Evans' absence.
"We always have speculation, we are used to it. Last year it was Sheffield Wednesday, previously it was Peterborough and Leyton Orient, there is always speculation.
"When you are successful you are coveted and people put two and two together.
"Obviously with Steve's family living in the town there is always going to be speculation there. We will just get on with the job like we always do.
"I don't know anything about it. I am sure I would be the first to know, we have worked together for a long time, it seems like longer.
"We have worked together for 10 years or so now so I am sure I would be aware of something.
"We are just concentrating on our job, it's a difficult enough job to try and get up that table with the start we have had."
