The South Africa international swapped Merseyside for North London for £3m during the January 2011 transfer window.
However, the 30-year-old has failed to establish himself at White Hart Lane after being held back by injury.
Pienaar was then loaned back to the Toffees in January, where he has earned rave reviews for a string of impressive performances.
Moyes has now revealed that he would love to bring the midfielder back on a permanent basis.
"It would be great to keep him," admitted Moyes. "He's found somewhere he is happy so hopefully we will be able to do it."
Pienaar has scored three goals in 10 appearances since his return to Goodison Park.