Seamus Coleman believes Republic of Ireland have a bright future under manager Martin O'Neill
The 64-year-old, assistant Roy Keane and the rest of the staff agreed new deals on the eve of the Euro 2016 finals, but are yet to put pen to paper.
But having seen them guide their side to within a whisker of the quarter-finals after Sunday's battling 2-1 defeat by hosts France, Coleman, named captain both at the weekend and for the famous victory over Italy, is hoping an extended stay can pay greater dividends.
The 27-year-old Everton full-back said: "I can't speak highly enough of both of them.
"Martin is the kind of manager that you really want to go out and do your best for him. He's a great motivator, great manager and he's one of those managers, as I said, you just want to go out and do it for him.
"It would be great if he could stay on because we've learned a lot from him."
O'Neill and Keane have ushered in something of a changing of the guard during their three weeks in France with vastly-experienced trio Shay Given, John O'Shea and Robbie Keane, who have amassed 390 caps between them, playing largely peripheral roles as the tournament took shape.
At the same time, Shane Duffy, Jeff Hendrick and Robbie Brady have emerged from the ranks to prove their ability to play at the highest level with Norwich winger Brady in particular making his mark with a dramatic late winner against Italy and a coolly-taken penalty which left France fighting for their lives at the Stade de Lyon.
He too is keen for O'Neill and Keane to continue the mission they launched some two and a half years ago.
Brady said: "I think it's very important. I think they've installed something into the team, installed belief and having us organised and wanting us to play a certain way, and I think that's shown here.
"To lock horns with some of the best teams in the world and give more than a good account of ourselves is a great credit to ourselves and the staff. I'll be delighted if they manage to get it done."
If Ireland's adventure ended in Lyon, it threatened to do so with a bang as Brady's successful second-minute spot-kick after Shane Long had been felled by Paul Pogba's clumsy challenge stunned a hugely partisan home crowd.
However, as fatigue kicked in - Didier Deschamps' players had almost a week to prepare for the game, O'Neill's just three days - Atletico Madrid forward Antoine Griezmann exploited it to score twice inside three minutes and when Duffy was dismissed for tripping him as he hunted down a hat-trick, the die was cast.
Coleman said: "We started very well and we'd full belief that we could have got something from the game. We played very well in the first half.
"But in the second half, probably our legs were gone a little bit and they were that little bit fresher I suppose, but...I don't know. It's just disappointing at the minute."
That disappointment will, however, eventually dissipate and 24-year-old Brady is already looking forward to the start of the World Cup qualifying campaign in September and the chance to play on an even bigger stage.
Asked if Ireland had evolved as a team during the competition, he said: "I think we always had belief that we were a good team.
"There were some disappointing results throughout the qualifying stages, but to show the guts and determination to come back and push through and then to come here and play against some of the best teams in the world and really show that we deserve to be here was extremely pleasing.
"But I think there are positives to be taken from this tournament going on now to the World Cup."