Verheijen was assistant manager under Coleman's predecessor Gary Speed, and is a popular figure with senior players in the national squad, including captain Aaron Ramsey and Craig Bellamy.
Verheijen tweeted earlier this week that his initial discussions with the former Coventry boss had been "positive" and although Coleman was keen to play down the significance of the meeting, he told BBC Sport Wales: "We're very much looking for that (Verheijen staying)."
He added: "But we've only had one meeting, so I spoke as much with Raymond as I did with (fellow assistant) Osian Roberts or anyone else - nothing special.
"People have made it into something that it's not, really. It was a productive meeting and we'll speak again. It was promising."
Source: PA
Source: PA