The Saints boss has been strongly linked with the vacant post at The Den following the resignation of Kenny Jackett.
Lomas still has a year of his contract to run at McDiarmid Park and he has just guided Saints to the qualification rounds of the Europa League for the second successive season.
"There has been no contact whatsoever from Millwall," Brown said in the Courier.
However, Millwall chief executive Andy Ambler revealed that the Championship club are willing to pay compensation to get their man.
And Ambler insisted the Lions will go through the correct channels when they wish to speak to another club.
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."