The Boys in Green play Erik Hamren’s side at the Stade de France on Monday June 13, but could be without Walters, who has not trained since last Thursday with an achilles injury.
The Stoke City forward was instrumental during Ireland’s qualifying campaign, scoring five goals - including a double against Bosnia and Herzegovina in the play-offs - and Keane claims that the 32-year-old has “earned” extra time to recover.
"That's the million dollar question," Keane told reporters when asked if Walters would be ready for Sweden. "There are certain players you would wait a little bit longer and Jon has probably earned that right for another few days to be given the benefit of the doubt.
"Sometimes when players are coming back from injury it's down to how positive they are and I think Jon is dying to get back involved.
"But I think he just might have to be a bit more patient and he might have to wait until near the end of the week.
"I mean he's one of the fittest lads in the group and I think that we probably won't have more news on Jon until later in the week."
Keane also addressed his recent criticism of several players after Ireland's 2-1 defeat to Belarus at Turner's Cross last week.
The former Manchester United captain's public assessment of a number of players' performances - in particular that of Aiden McGeady - led Martin O'Neill to suggest that Keane's words were "slightly on the strong side."
Keane refused to detail the nature of his conversations with those players but did say that he has spoken with them, and that he’s used to addressing players.
"What I say and don't say to the players is private," stressed the Cork native. "I've spoken to the players, a few of the players, not just Aiden, but I've done that throughout my career.
"When I was a manager at Sunderland and Ipswich I had no problem in speaking to players, staff members, if I feel I've gone overboard.
"So that isn't an issue for me but I'm certainly not going to go into any conversations I've had with the players."
Norwich City's Robbie Brady sat out Tuesday's session as a precaution after suffering a back spasm on Monday, while Robbie Keane completed the full training routine as he strives to regain fitness ahead of June 13.
Everton midfielder James McCarthy, meanwhile, is back to full fitness and is expected to be in contention for Ireland's Group E opener against Sweden.