The Real Madrid forward rates Coleman as one of the best managers he has ever worked with and the entire squad want to ensure that the 47-year-old is fully aware of how they hope he will rethink a previous prediction that this would be his last campaign.
"Of course we want him to stay", Bale said.
The loss against Ireland was particularly hard to take for Coleman, as it marked the first defeat Wales have suffered in a competitive fixture since they lost 3-0 to Serbia in September 2013 in the qualifiers for the 2014 World Cup.
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Kaepernick said at the time that he was protesting the treatment of black Americans, particularly by the police. There were other steps Kaepernick took that did not receive the same amount of attention as his anthem stance.
Those talks are set to take place ahead of a planned November home friendly, probably against Mexico or the United States.
Chris Coleman will determine whether he can take Wales forward before making a decision to stay or call time on his "dream job" and has the backing of star striker Gareth Bale to carry on in the role he's held for almost six years.
"There's a chance I can and a chance I won't", Coleman said when asked if it was possible he could continue in a job he has held since January 2012. I can't give an answer right now.
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'The message from the whole squad would be that we want him to sign a new contract'.
"It's six years I've been in charge, or coming up to it at Christmas, and I can't say right now about my future because I'm not thinking about it". I think he will be lined up for a big job, if that is what he wants. "When the dust settles we'll see where we go", he added. Wales had to win their last four games, they won three and just came up a little short tonight.
"What we've got in the dressing room the opportunity is there for Chris or whoever else to take this team onwards, " Roberts said. "But our players have done brilliantly and we've got to learn from it".
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On the other side, Cubs Manager Joe Maddon said the club would stick with Tuesday starter Jake Arrieta if the game is bumped back. Going back to the regular season, he is 5-2 with a microscopic 0.74 ERA and 73 Ks in 60 2/3 innings over his last nine starts.
It was not to be for the Dragons, though, as James McClean struck in the 57th minute to send Ireland through to the playoffs.