Toffees boss calls for misfiring strikers to up their game
The South African international's contract expires during the summer and the Toffees boss has already admitted that the club may be forced to sell the player in January to raise funds for transfers, instead of losing him for free just months later.
Goal.com UK also exclusively revealed that the Merseyside club are targeting fellow South African Siphiwe Tshabalala as a replacement, should Pienaar opt not to sign a new contract and instead be sold to another club.
However, for now, Moyes maintains that there is still time for Pienaar to continue his stay at Everton, should the player decide to do so.
"I'd like to think we could see if there's room for manoeuvre," he told reporters.
"I've tried to leave the door open as long as I can. We'd be delighted to keep him."
The former Preston North End boss also took a swipe at his forwards, presumably in the hope that public criticism may see them rise up to the challenge of hitting the back of the net more often.
"Louis Saha was through against Blackpool, 'Becks' [Jermaine Beckford] was through in one of the other games - that isn't luck, that is bad finishing," said Moyes.
"That is more to do with the way the results have been going rather than luck.
"We have never got that momentum we talk about. We need to try to find it, we need to try to get ourselves away from the wrong end of the table and start getting closer to the teams at the top.
"How do you win if you don't take your chances?
"That is football, we have to keep going. We have to keep creating the chances and hopefully convert them."