I doubt Nokia would sell the brand. Nokia has been a Finnish company for 150 years. They made several mistakes - including bringing Elop in - and they probably wanted to get rid of the part of the company that was no longer sustainable.
But I doubt they ever wanted to give up the brand, based on the details I read these days about the deal with Microsoft (only sold the mobile division, licensed the Nokia brand for several years, banned from producing mobiles only until 2018, etc).