The 22-year-old has shone in south London this season and was voted the club’s best player of the campaign at the end-of-season awards night, with Palace understandably keen to keep the Chelsea player on loan .
Gallagher has eight goals and five assists to his name which helped him get called up to England and the fact that next season’s World Cup is in December could impact the midfielder’s decision .
Blues manager Thomas Tuchel has spoken enthusiastically about the Cobham academy graduate but there is no guarantee he will make his way into the starting line-up at Stamford Bridge.
Speaking ahead of Palace’s trip to Aston Villa, Vieira said of Gallagher’s future: “It’s up to Chelsea and of course the player.
“We have him for the year and we’re really happy with his contribution, he’s been great. Then after the season he goes back to Chelsea and the decision is up to Chelsea and Conor.
“A lot has already been said. He played I think his best football at this club, which allowed him to go to England. It will be important for him to ask a question about what the next step will be for him and the next step can be at Chelsea because he has to go back and see how things will go for him.
“Of course we are and I’m really happy with the year we’ve had together. He’s been really good to us and we’ll have to wish him well if he returns to Chelsea. If there’s a possibility to bring him back, we will definitely talk about it.
Gallagher was one of two Palace players nominated for the Premier League Young Player of the Season award alongside Tyrick Mitchell.
Both have been regulars under Vieira, who saw the duo and centre-back Marc Guehi make full debuts for England during the campaign.
“Conor and Tyrick have been really good this season,” he added.
“They played week after week and performed very well. Both have been called up to England, so that’s a huge step forward.
“I think it’s good for the club as well as because it shows we’ve done some good things this season. To have two young players nominated is good.
Vieira was Palace’s other representative in the Premier League nominations as he is in contention for Manager of the Season.
In his first season at Selhurst Park, he guided the Eagles to an FA Cup semi-final and they could reach a club-record Premier League points total.
“It’s always good to be nominated for this kind of award,” Vieira said.
“To be nominated I think everything has to go well (for) the club, the players have to perform well and it’s good to show what you achieve in the season.”
Additional PA Sport reporting.