The position became vacant after the death of Gary Speed in November and Verheijen, who served as the 42-year-old's assistant, has claimed it was Speed's wish for him and fellow coach Osian Roberts to take over the side ahead of qualifying for the 2014 World Cup.
Hartson initially said that it was an "absolute disgrace" for Verheijen to make that claim on Twitter and said he could not work with someone who wanted the top job.
But the 36-year-old has since reconsidered and told BBC Radio 5Live: "Raymond has come out in the past and put it on Twitter that it was Gary's wish that himself take the country forward.
"If that is what the FAW want and it means myself going in as a front man and the manager, absolutely, of course I would work with Raymond and the current regime if that's what it meant for me to manage my country.
"I don't think I'm in a position to call shots here; it would be my first job and I would be honoured to do it.
"I actually called Raymond a disgrace, which I take back. I don't think it would be an issue to go in as a leading man, that figurehead."
That was a far cry from Hartson's initial stance, with the former Arsenal, West Ham and Celtic striker being strongly critical of Verheijen.
Speaking to talkSPORT he said: "How can you work with somebody who wants your job? There is no way you can do that.
"Raymond wants the job. He has publicly stated it was Gary's wish for himself and Osian to take this country forward, which was an incredible statement to put on Twitter. What on earth did he mean it was Gary's wish?
"Gary's wish was to take this team forward. But for Raymond to come out and say that publicly was an absolute disgrace. He has publicly stated that he wants the job, how on earth can you go in and take a job knowing that your number two, your most trusted ally, wants your job? You cannot work with that person."
As for his own credentials, Hartson added: "I was asked last night who would I appoint and I said myself. I was interviewed for the job this time last year so I don't really know what has changed since then.
"I have a lot of support out there. I tick a lot of the boxes. But I also understand as well that I don't fit the criteria. In terms of the experience, Chris Coleman is way ahead. He has managed in three different countries, Fulham in England, Spain, and he's just come back from Greece.
"The only thing going against me is my lack of experience. But you look back at Mark Hughes. Mark Hughes' first job in football was the Welsh job. He was younger than myself, he was 34. He went straight into the job and look at what he's done."