After losing in five games to the Miami Heat in the second round of the playoffs, Kidd talked to ownership about a dual role.
He is entering the second year of a $10.5 million deal.
By comparison, Steve Kerr and Derek Fisher, both new coaches without any previous coaching experience, recently signed five-year deals worth $25 million each with the Warriors and New York Knicks, respectively.
Kidd's uncertain future casts a cloud over the Nets as free agency begins Tuesday. The Nets hope to re-sign Pierce and Shaun Livingston, both staunch Kidd supporters.
Also, it remains to be seen how Kidd's uncertainty affects Garnett's decision to return for a final season with the Nets. Garnett has given indications of coming back and is planning to begin preparations for the upcoming season starting next month.
The Lakers are the only team in the league at present with a head-coaching vacancy, but sources close to the situation told ESPN.com that Los Angeles will not be reaching out to Kidd as a potential candidate if he indeed becomes available.
ESPNNewYork.com's Ian O'Connor contributed to this report.