Arsenal have missed Sanchez for their Community Shield triumph over Chelsea and their 4-3 Premier League opener against Leicester due to an abdominal strain.
The Chile international is expected to miss the trip to Stoke on Saturday (5.30pm), but Parlour is confident he will be back to face Liverpool the week after.
Parlour said on talkSPORT: “I know the fact he’s working so hard to be fit, he came back that little bit later, it takes a little bit longer to be ready for the first team.
“I don’t’ think he’ll be playing against Stoke but I’m sure he’ll feature against Liverpool in the next one.”
Sanchez has been heavily linked with a move away from Arsenal this summer, with just under a year remaining on his contract.
But Parlour can’t see the former Barcelona man trying to force through a move.
On the possibility of Sanchez handing in a transfer request, Parlour added: “I don’t think so. A lot of deals are done last minute anyway.
“It’s a game of poker, where people are saying ‘we want this for him’, ‘we’re going to offer this’ and right at the last minute they come to an agreement in the middle.
“So whether that happens with Alexis Sanchez, we’ll have to wait and see.”
Manchester City and Paris Saint-Germain have both been linked with Sanchez – but Parlour reckons they’re already well-stocked with left-sided forwards.
The former Gunners man added: “I think Arsenal put a really good offer on the table, for me the only clubs really who can afford him is PSG or Man City.
“But PSG have just bought Neymar, so why would they want the same sort of player? And Man City, look how many players they’ve got to fill those sort of positions.”