Current AM for Wrexham, Lesley Griffiths has said that the sign, above Mr Marek's former office on Regent Street should have been taken down months ago.
She said Dr Marek should 'Accept his defeat' and take the signs down.
But he has responded
by saying that if Ms Griffiths had contacted him about it, he would have had the sign painted over.
A Welsh Assembly spokeswoman said that although the assembly has no legal power to remove it, they are writing to the former AM, asking him to arrange for it to be taken down.
She said: "Although, we have no legal power to remove the sign, we are suggesting to him that he removes it because it is misleading the public."
A spokesman for the Liberal Democrats said that North Wales AM Eleanor Burnham has been moving in to the Regent Street office and will officially work from there from December 3.
Ms Griffiths, said: "I have received several complaints from constituents over the fact the signs remain in place.
"The returning officer from the assembly elections has also expressed her concern to me that Mr Marek is publicising that he is still the AM for Wrexham.
"It is obviously confusing for the public. Six months have elapsed since Mr Marek was defeated in the Assembly Election.
"The time has come for Mr Marek to accept his defeat and take the signs down immediately."
Dr Marek said that should Ms Griffiths have contacted him about it, the issue would have been resolved and he would have painted over it immediately.
He said the sign will be painted over shortly.
He said: "If Ms Griffiths had contacted me about it, of course I would have put some white paint over the sign.
"At the end of the day, I know I'm not the AM and it should be painted over ."
Dr Marek said that he is still contacted about Wrexham issues. He said: "People still contact me about various things and I then refer them to the five AMs for Wrexham and North Wales."
The full article contains 383 words and appears in Evening Leader Wrexham newspaper.