Fenlon was forced to retire midway through the Leinster SHC clash against Kilkenny with damaged ankle ligaments.
His training has been seriously curtailed in the interim as he concentrated on maintaining fitness in the gym.
Manager Seamus Murphy is prepared to give the 1996 All-Ireland medal winner every opportunity to prove his fitness.
"Last Sunday was the first time Adrian actually put on his boots since the Kilkenny game," Murphy said.
"He did some light training and pucked the ball about, but it's still some way to go before deciding on his fitness.
"We're delighted he had made such progress, so we're prepared to wait as long as possible. He has made a huge effort to try to get back to full fitness for the quarter-final.
"There's some light at the end of the tunnel but it's uncharted territory for Adrian over the next few days. We just have to wait and see, put him through his paces and see how the ankle reacts."
The Rapparees star only returned to the side for the championship, having missed the league campaign owing to exams.
"Adrian is crucial to us in midfield. His ability to play accurate ground ball into the forwards is a vital part of our game, particularly against what is a very physical and strong Clare defence, who pride themselves on their man-to-man marking. He's a huge part of our game plan.
"It's acknowledged he's one of the best ground hurlers in the game. Not just that, he brings a real solid formation to midfield, playing so well just in front of the half-back line. It may be less than 50-50 at the moment, but we're keeping our fingers crossed he'll come through later in the week," added Murphy.
With or without Fenlon, Wexford are going to have to come up with a game plan that allows their skilful but slight of stature forwards to make inroads against a physically imposing Clare back line.
Their lack of size has been held up as a failing before, but corner-back David O'Connor one of their few players able to eyeball Clare's tallest is confident that Wexford's attackers can cope.
"We are a small enough team, but you can't put a fella in just because he's big. We might not have too many six-footers playing but I've marked some of our smaller fellas in training and they're well used to coming up against lads bigger than them. They're well able for it."
Wexford approach Sunday's game on the back of a hugely encouraging display against Kilkenny in the Leinster final but putting back-to-back performances together has been largely beyond them in recent years.
Sunday's tie in Croke Park offers them another opportunity to lay that particular bogey to rest, although Clare were comfortable winners in Portlaoise three years ago when the teams last met in the championship.
"I suppose, after Kilkenny, we know when we play as well as we can we're a match for anyone.
"Our problem has always been putting together two performances in a row. We haven't done that in such a long time. Maybe it's a mental thing.
"We have talked about it. We had a fairly consistent league this year until we played Kilkenny and Clare but I suppose we've been on a bit of an upward curve again since those games."