Wenger approaches the 20th anniversary of his time in charge at Arsenal still eager to end his 12-year wait for a Premier League title.
And Bergkamp, currently the assistant manager at Ajax, could be well-suited to taking the mantle in a post-Wenger era, with another club legend as his assistant.
"If he goes, when he goes, whether that's a year or five years, we should probably take an old player," Limpar told Standard Sport. "Tony Adams maybe. Or Dennis Bergkamp.
"A lot of old players could take over, but Arsene's not done yet. When the time comes we should pick a high-profile player.
"Why not Dennis? He'd be great. Take him and Thierry Henry as an assistant. They know the system, they know the club."