"If you bring in a new manager things will change," said Verheijen.
"What we are looking for is not a new manager with new ideas and new people.
“It is a matter of respecting Gary's legacy so I think it is the responsibility of the FAW to find the right person who fits in the current structure and is willing to adapt to the current set-up”
Raymond VerheijenWales assistant coach
"And if the FAW make a decision basically they turn their backs to Gary Speed and go in a different direction - and I think that will be very disrespectful and insensitive.
"We need a figurehead who is willing to adapt to the current backroom staff and set-up because everyone can see we that we have developed a winning formula."
Wales won four of their last five internationals before Speed's shock death in November and
Wales made the biggest leap
in the Fifa rankings in 2011 as they moved to 48th place from 113th in the world.
Asked if the current backroom staff would work with bookies' favourite Coleman, the Dutch coach said he "didn't think it was appropriate to speculate about names".
But Verheijen did state: "I think what we are looking for a figurehead maybe a Wales legend like Ryan Giggs and Ian Rush who are willing to be the figurehead and protect the Wales identity and adapt to the current structure.
"Normally when a manager is sacked and a new manager comes in, the backroom staff have to adapt to the new manager but this is a totally different and a very delicate situation.
"If someone steps in and starts to change things he will risk that things go down and that is not a good idea at all.
Coleman keen on Wales job
"It is also a matter of respecting Gary's legacy so I think it is the responsibility of the FAW to find the right person who fits in the current structure and is willing to adapt to the current set-up."
Premier League champions Manchester United have turned down the Welsh FA's request to talk to former Wales captain Giggs about succeeding Speed,
offering Giggs a new playing contract
, while Wales' record goal-scorer Rush has also been linked to the vacancy.
Verheijen, who has helped coach the Netherlands, Russia and South Korea at World Cups, said his Wales contract is until 2014 and revealed he "never applied" to be the next national team coach.
The Football Association of Wales has assembled a six-man panel, led by president Phil Pritchard, to appoint Speed's replacement.
No discussions have taken place with any potential candidates, according to the FAW, and chief executive Jonathan Ford has said it is "too early" to say whether an appointment will be made before their
next friendly with Costa Rica
in Cardiff on 29 February.
Verheijen also announced his inaugural UK Football Academy symposium at Emirates Stadium has been renamed The Gary Speed Football Congress as a tribute to his former manager who had been due to speak at the 8 February event.
The Gary Speed Football Congress is set to become an annual fundraising event and is supported by Speed's friends and former Newcastle United team-mates Shay Given, Craig Bellamy and Alan Shearer.
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