Right-back Chris Gunter said: "Everyone in Wales - fans and players - would want to see him 100 per cent carry on being the greatest Welsh manager of all time".
"He's been a massive part of what we've done and he is the man to hopefully take us forward".
With Wales planning a November friendly - Mexico and the United States top the list of possible opponents in Cardiff - Coleman plans to holds talks with the FAW about his future in the next few weeks.
The squad have given their unanimous support to Coleman and it is also understood that the Football Association of Wales is hoping Coleman extends his stay at the helm.
"Chris is his own man and he'll eventually decide what is right for him and for Welsh football", said Roberts.
The 47-year-old was always planning on ending his time with the Welsh national team at the end of the current campaign, though he had hoped that would be in Russian Federation rather than Cardiff, as his side fell 1-0 at home to Ireland to miss out on a World Cup play-off spot.
Coleman has been in charge of Wales since 2012, and memorably roared the Dragons into Euro 2016 - their first major tournament in 58 years - and then remarkably through to the semi-finals where they lost to eventual champions Portugal.
Last night, in the immediate aftermath of the devastating loss, Coleman admitted that he is undecided on whether he will stay on as Wales boss but Sky Sports is reporting that Gareth Bale and other senior players in the Welsh camp had a meeting with Coleman to convince the 47-year-old to stay on.
But his stance appears to have softened and he may be open to leading Wales in their bid to qualify for Euro 2020. "He has said you're lucky if get you one opportunity in a lifetime to do it".
"I am sure this will be my last campaign whether we qualify or not".
"The whole nation will be mourning and disappointed because, again, that elusive World Cup has passed us by".
"We will wait to see if he feels if he can take this team further".