Gallagher’s standout loan spell in south London last season earned him his first England call-up, but the 22-year-old played just one minute of Chelsea’s season opener at Everton.
His former boss did not rule out a reunion, but pointedly reminded everyone of the process.
“This is not our decision,” said Vieira. “It has to be made by Chelsea if the player is available, then Conor has to make a decision.
“We’re just like any other club, focusing on players who are available and here, the situation is not in our hands, there’s no control so it’s pointless to talk about it.”
Gallagher, who scored eight goals across 34 appearances for the Eagles, will be in the market for more playing time as he campaigns for a place in Gareth Southgate’s Qatar-bound squad.
Asked if the unusual timing of November’s World Cup has also affected transfer window negotiations, Vieira replied: “It’s not just Conor, it’s players who want to have a chance to go to the World Cup want to play games.
“There will be a question about what is in their best interest but this is a player’s decision. If they are available then we will show interest, who knows.”
Palace lost the Premier League curtain-raiser 2-0 to Arsenal and will continue their tough start to the 2022-23 campaign when they travel to Anfield to face Liverpool on Monday night.
“Everybody in the game knows that stadium,” said Vieira. “It is a special ground. The atmosphere is one of the best in Europe. Players will be excited, you want to play in those kinds of stadiums where the atmosphere is strong.
“It’s going to be challenging but there is excitement and pleasure to play in these stadiums more than anything else.
“I don’t have any doubt about the character and personality of my team. We will play our best, it may not be enough but we are not going there to be shy or hide – it will be challenging but we are ready to face those challenges.”
The composed Eagles boss also looked forward to meeting his opposite number on the sidelines, Jurgen Klopp, and expressed his admiration for the animated German who will lead the hosts on Monday.
He added: “His personality, he’s got a presence on the bench. It doesn’t change anything for me.
“It’s not about the managers, it’s about teams trying to win matches. His career has been fantastic, he’s won almost every single trophy and the way he develops players is really exciting.
“He has his destiny and mine will be what it will be. I admire him for what he’s been doing in the game in Germany. That’s it.”