St Johnstone chairman Steve Brown insists Millwall have not approached him to ask permission to speak to McDiarmid manager Steve Lomas.
The Perth boss has been strongly linked with the vacant post at the Den and has been installed as short-odds favourite with several bookmakers ahead of others such as Markus Babbel, Alex McLeish and Uwe Rosler.
Lomas still has a year of his contract to run with Saints.
However, Millwall chief executive Andy Ambler revealed that the club are willing to pay compensation to get their man.
He also insisted that the Lions were determined conduct their business in the proper manner and, if they were interested in speaking to a manager still tied to another side, they would do so through the correct channels.
Ambler said: “We’ll do things properly. We are going to be consistent with how we would want to be dealt with.
“We’ll make sure people who are interviewed are done so in the right way. But we’re not afraid of paying compensation if we have to.
“If we think someone at another club is the right man for the job, we’ll deal with that.”
However, Brown told Courier Sport that: “There has been no contact whatsoever from Millwall.”
Lomas has also distanced himself from links with the job and instead is focusing on Saints early start to the season in their Europa League qualifier.