The Orchard County will attempt to bounce back from their disappointing Ulster championship defeat to Donegal with a win over Wicklow in the qualifiers.
But even if they pick up a first Championship win under Kieran McGeeney, there remains question marks over their ability to battle it out with top teams.
McConville and McGeeney were playing colleagues in 2002 when the county won its only All-Ireland title.
But 13 years on, McConville said it may be the case that they simply aren’t good enough to challenge the top sides despite last year’s promising run to the quarter-finals.
“Maybe there were signs that the performance against Donegal was coming,” said McConville. “They struggled to put away Fermanagh twice in the league.
“We also finished the league with a disappointing result against Sligo. And we had a disappointing performance and result against Cork in a challenge match.
“So maybe in many ways the writing has been on the wall and maybe this is where we are at. Maybe we shouldn’t be challenging the likes of Donegal at this moment in time, maybe there is more work to be done.”
The Crossmaglen man believes that McGeeney won’t dramatically alter Armagh’s style of play against Wicklow despite the Donegal result.
“They’ll stick to what they’ve been doing,” he continued. “I don’t think they’ll be for changing or turning. I think the trick for Kieran now is just to get the players to play.
“I don’t think a lot of things will change at all. I haven’t spoke to too many of the boys since the Donegal game. But I’ve absolutely no doubt they’ll be gutted with the way they played.
“They felt as if they were prepared for that game. A lot of work had gone in to that Armagh team so I can’t see them just going in a different direction after one game.”
Similarly, McConville doesn’t believe that McConville’s reputation has been tarnished by the dispiriting start to his Championship tenure.
‘Geezer’ was privately credited with being a huge influence on Armagh last year when they reached the All-Ireland quarter-finals and his upgrade to manager was widely welcomed by supporters.
“It’s probably too early to say something like that,” said McConville of McGeeney’s reputation.
“And the other side of the coin is that the players have to take a lot of the flak for what went on against Donegal.
“It’s one thing managing but when you send players out there, they have to perform. That was the thing that let Armagh down, they went out and they weren’t able to perform for whatever reason.”