Zaha, 28, earlier this summer again made clear his desire to leave his boyhood club to chairman Steve Parish, but there has been little interest in the Ivory Coast international and Crystal Palace's valuation remains higher than that of any potential suitors.
Since Vieira's appointment at Selhurst Park, the Eagles have invested impressively with Michael Olise, Marc Guehi and Joachim Andersen all signing while Conor Gallagher has arrived on loan.
The French manager is hopeful that their investment is enough to convince Zaha he is in the right place at Palace and has held talks with his star man.
"I'm aware of Wilfried [Zaha’s situation] in the last couple of years but we had a really good conversation and I'm looking forward to working with him," Vieira told Sky Sports.
"He's one of the most talented players in this league and we don't want to lose one of our best players.
"All the players are smart enough to see what the club is trying to build and where the club want to go - we've made some really exciting young player signings and I think that shows the direction the football club wants to take.
"I hope Wilfried will be part of that, I don't have any doubt about that, and I am looking forward to working with him and trying to take Palace as high as we can."
Palace's stance on keeping Zaha, who again left his agents earlier this summer, was only made stronger by the injury to Eberechi Eze late last season which saw him ruled out until January, while Olise arrived with a back issue and is likely to miss the start of the new season.
Palace have moved on a lot of experienced players this summer with Gary Cahill, Andros Townsend and Scott Dann a number of older players to leave and make way for the younger players arriving.
While there is excitement over the potential of those who have been signed, Vieira is urging patience.
"We are an ambitious football club and want to challenge as high up the table as possible," Vieira said. "We believe we have a good squad but at the same time we have to realise some of the players will need time to express themselves at this level.
"We can be excited about the young, talented players that we are developing but we need to manage expectations.
"The Premier League is challenging and we're going into a new cycle where we have lost some experienced players and are bringing in some young, talented players who don't have Premier League experience.
"So we'll need a little bit of time to make everything work and find the right balance."