Interim coach Desiree Ellis this past weekend guided Banyana Banyana to COSAFA Cup glory after a victory over hosts Zimbabwe in the final for the nation's fourth triumph in the event.
Ellis, who was handed the reins in October last year following the departure of Vera Pauw, became the first South African to win the competition as a player, in 2002, and coach.
Tovey said the decision to appoint the Banyana coach rests with SAFA president Danny Jordaan and CEO Dennis Mumble.
"There was process that has gone through with regards to three people as finalists for the position. That was left up to the negotiating from the president and the CEO," said Tovey at a media function on Wednesday.
"Desiree has certainly done wonderfully at the COSAFA tournament and has shown that she is learning very quickly.
"But it's not only about throwing her in the deep end too quickly. We want to give her time to learn and grow. Obviously now we've got to engage and see where we are now with the people that we've chosen.
"It's not only that you can go and select the person that you want. There's still financial negotiations that have to take place."
The former Bafana said the contenders are from South Africa and abroad but would provide no further details.
"Both on the list, there's a South African and a foreigner," he said.
"But we need to see how we can go forward on this matter. I can't mention names at this moment in time, it's not my duty to do so.
"We're trying to equip our South African coaches that if you did bring in a foreigner coach, I'm not saying we are, how can our South African coaches learn from foreign coach at that stage?
"Are our South African coaches at the level to take over after we have fully finished the process going down the line? So there's a lot of thought processes.
"Maybe Desiree is ready right now, that decision will be made."