Scot would rather player see out his contract than sell him in January
The South African winger's current contract is set to expire at the end of the season, and he is yet to sign a new contract with the Merseyside club.
With Tottenham Hotspur thought to be hovering over the player to acquire his services, there has been some speculation that the 28-year-old could choose to leave on a Bosman transfer.
And Moyes, who signed the midfielder for £2 million in 2008 – after a season-long loan at Goodison Park – believes he would rather have the player available through the season than try to sell him during January.
"If it came to that, then I said I would be happy for it to run down if he didn't want to sign," he said in the Daily Star.
"For what we paid it was definitely worth it.
"I'm hoping he would choose to stay. If he doesn't, then that happens."