Wales missed out on qualifying for Russian Federation by finishing third in their group behind the Republic of Ireland, who beat them into the play-off spot with a 1-0 victory in the final game last night.
"After the game he thanked us for our efforts over the last 10 days, but I think everyone in Wales - fans and players - would want to see him 100 per cent stay on".
Chris Coleman has been convinced to rethink standing down as Wales boss but remains tempted by a return to club football, The Independent understands.
The Real Madrid man said: "Of course we want him to stay".
While Welsh football was consistently on a positive trajectory, Monday's loss will come as a major blow to Coleman and the team.
Apparently Coleman does still very much have the backing of his players, as Sky sources claim, he was met by senior stars such as Gareth Bale who urged him to stay on as boss.
"There is no question that he is the best manager in Welsh history and nobody wants that to end".
"He's been a massive part of what we've done and he is the man to hopefully take us forward".
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Chris Gunter said everyone in the country is praying Coleman won't walk away.
"He has said you're lucky if get you one opportunity in a lifetime to do it". FAW Chief Executive Jonathan Ford is understood to have told Coleman that he wants him to commit to a new contract and hopes to sit down with the 47-year-old before their friendly fixtures scheduled for November.
"Whatever decision he makes it's going to be a very hard one, but this is the dream job managing your country".
Wales reaching the Euro 2016 semi-finals was an achievement well beyond expectations but there is a feeling that, with Gareth Bale and emerging young players, the side could also do well at Euro 2020. "We will wait to see if he feels if he can take this team further".
Next summer's tournament in Russian Federation will mark the 60th anniversary of Wales' only previous finals appearance in Sweden.
Welsh supporters would have woken up this morning wondering how they are not in a World Cup playoff.
"We've all had disappointments in football before and you get a lot more lows than highs".