Pienaar spent the last six months of last season on loan at Everton, just a year after leaving the club in favor of Tottenham Hotspur. The 30 year old impressed in his loan stint, and both Tottenham and Everton are now looking to make the deal permanent. A potential dealbreaker could be the £5million asking price Spurs have slapped on the player.
With Harry Redknapp leaving and Andre Villas-Boas replacing him, the pecking order of players at White Hart Lane is uncertain at the moment. This has not stopped Moyes from setting his sights on the South African international, as he has now finalized a deal to bring striker Steven Naismith to the club from Rangers.
"We are keen [on Pienaar] and I hope in time we would be able to conclude that deal," he said. "I don't know if the situation has changed [with Villas-Boas coming in as new Spurs manager] but Steven has made it very clear he wants to come back here and my understanding is that hasn't changed.
"My next job in the coming weeks is to get Steven Pienaar here as well. The season we qualified for the Champions League we had people in place early doors so if we could do that again then we would hope we could replicate what we have done before.
"The Premier League has changed in the level of squads and the standard but we will try to start the season better than we have done."
Moyes also commented on the transfer statuses of his key players, with Everton reportedly looking to cash in on their stars in an attempt to overcome financial troubles.
However, Moyes has dismissed speculation that bids are being made for his stars, including defender Leighton Baines and midfielder Marouane Fellaini.
"I've heard nothing from nobody," he asserted. "We are always going to have interest in the players we have because we have good players but we don't sell easy here and we try to build a team.
"Of course you are going to lose players now and again but we have kept the bulk of players and we will continue to try to add to it and keep improving."
Everton open their season against Manchester United, at Goodison Park.