Coleman has agreed terms on a two-year contract extension with the Football Association of Wales, although he has yet to put pen to paper.
But the former Fulham boss finds himself under pressure after three successive World Cup qualifying losses against Croatia, Macedonia and Serbia, the latter of which saw the Dragons slump to the bottom of the Group A table with two games remaining.
Despite seeing his side booed off following Tuesday's 3-0 defeat to the Serbs in Cardiff, and sections of the crowd demanding his removal, Coleman was adamant he is the right man to lead Wales.
And former Liverpool, Juventus and Wales striker Rush, who won 73 caps and scored 28 goals for his country, believes the FAW should stick with him.
Rush, who hosted the FAW Community Awards presented by McDonald's at Cardiff City Stadium on Tuesday, told Press Association Sport: "You have to back him. In the modern game, people can be guilty of looking for instant success, and success sometimes does not happen.
"But who is going to do it instead of Chris, if they want someone Welsh in charge?
"Give him another two years and see what he can do. It starts from now, if we are serious about doing something for Euro 2016."
He added: "They were tough circumstances in which he took the job (after Gary Speed's death), but you have to move on, although it can be easier said than done.
"I thought we could finish second in this group, but it has gone now and the result in Serbia last year was a big blow as it is not great to be three games in thinking you cannot qualify.
"You have to give supporters hope which is why finishing on a high would be a boost for a Euros where a larger number of teams will qualify, and we want to have a good seeding for that.
"Do that and why can't we qualify for 2016?"
Rush also believes Wales have enough young talent in their squad to be a more competitive proposition during the next campaign, although he admits Craig Bellamy's impending retirement from international duty is a blow.
He said: "Adam Matthews has done well and is learning at Celtic, Jonathan Williams is another one who looks a talent and they have stars in Aaron Ramsey and Gareth Bale.
"Looking head to 2016 there will be plenty of good players who have been in this team for a while.
"The difference will be that Craig Bellamy will not be there. We have players like Simon Church, Sam Vokes and Hal Robson-Kanu, but they are all similar.
"We need target players because we cannot rely on Bale and Ramsey all the time. Someone else has to be able to step up and get a goal."
Of Bellamy, he added: "He has been a fantastic servant for Wales, he knows what he has to do and he has been helping out the younger players.
"He has done well for Cardiff but he cannot play every game and it shows his commitment to Wales that he has kept turning up when he doesn't know what it may do to him fitness wise."