Wales haven’t made it to the finals of a tournament since Cliff’s great team of 1958 reached the quarter-finals of the World Cup in Sweden, where they were beaten by Pele’s Brazil.
Qualification has changed for Euro 2016 and now the top two teams from each of the nine groups will go straight through to the finals in France, joined by the best third-placed team and the hosts.
The remaining third-placed teams will meet in play-offs for the final four places.
Wales currently top Group B and face a huge game against pre-group favourites Belgium on Sunday.
“In my time there was a commitment and a team spirit and Chris Coleman has brought that back into the side,” said Cliff, capped 59 times.
“When they go onto the pitch they fancy their chances now, there is great confidence and spirit and that’s sweeping through to the supporters.
“Wales have a shout now. We’ve been in decline but we’re now we’re emerging again and teams are starting to take notice of us again. It will be a great game against Belgium and we might just get something.
“It would be fantastic for the country and Welsh football to make it. Wales is a rugby-dominated nation but it’s great to see the soccer side stepping up and getting some of that limelight and expectancy back. It’s looking good again.”