The former Roten attacker claims he advised the Bavarians to snap up his compatriot when he was still a relatively-unknown teenager at Santos
The Brazil international was heavily linked with Bayern ahead of the 2013-14 campaign, but eventually left Santos for Barcelona in a €57 million (£50m) deal this summer.
Elber admits he pushed for the current European champions to make a move for the forward but revealed the club opted against a big-money bid over fears Neymar would struggle to continue developing as a top player.
"Neymar was already on a different level than all of his peers at the age of 16," Elber was quoted as saying by Welt.
"But he was already quite expensive as well due to his contractual obligations.
"Bayern talked about signing him long and hard, but eventually opted against a transfer. Nobody knew whether he would keep on developing like he did at the time."
Neymar, 21, has been in strong form for Barcelona so far this term, netting four goals in 11 La Liga appearances.