The Stoke City forward, 32, has been dogged by an achilles problem lately – he started Ireland's 1-1 draw with Sweden at the Stade de France in their Group E opener but was substituted after 64 minutes and then sat out Saturday's 3-0 loss to Belgium in Bordeaux altogether.
"Hopefully he can do something. It's still very much touch and go. If you speak to the player he's improving every day but the game is coming up quickly," said Ireland assistant manager Roy Keane at a press conference at the team's base in Versailles, near Paris, on Monday.
Walters has scored 10 times in 40 appearances for his country and without his support up front Shane Long toiled against the Belgians as Martin O'Neill's side were outclassed.
"We know the type of lad Jon is and I think if there's any chance he thinks he can get through it he'll have a go," added Keane, who said he was keeping his "fingers crossed".
"Even if we managed to get Jon on the pitch for an hour it'd be fantastic. Of course you have to look after the player's welfare – if he doesnt feel right it's highly unlikely he'll be involved."
Ireland head into the game in Lille propping up Group E but a win against Italy – who are already certain to advance to the last 16 as group winners – may be enough to take them through.
Keane added: "We had a bad day at the office the other day. We have had setbacks before and we're looking forward to the match.
"We had a few plaudits after the first game but we knew we had to move on quickly.
"You have to deal with the setbacks and the disappointments because football is more about that than the good days. I think we'll be fine and come Wednesday we'll be ready."
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