Richardson, currently Port's director of coaching, was interviewed by the Saints on Wednesday night and is now the clear favourite to win the job.
But St Kilda might need to negotiate the outcome with the Power before making the announcement.
"He's on contract to us til the end of 2015 and that’s the way it stays and to leave it so late is terribly disruptive," Koch said on his Sunrise TV program on Thursday morning.
"If St Kilda want that to change they're going to have to talk to us as a club because we're going to stick with it. We're not going to release him."
Koch fired a salvo at the Saints, branding it a club in "turmoil".
"We made an offer to match what he (Richardson) is getting at St Kilda.
"The St Kilda board is meeting this morning, but they should take on that he's under contract until 2015.
"Why should we as a club be disadvantaged because of St Kilda's issues?
"Yes, they're a club in turmoil, but they shouldn’t put other clubs in turmoil and look for a replacement. Get your act together."
Richardson had initially declared no interest in the Saints job but changed his mind late on Tuesday night when the club indicated he would be the frontrunner if he threw his hat into the ring.
