The German has been linked with a move from Opel to Audi, which would see the former Volkswagen Group manager return to his former employer.
Neumann, 56, who has restored Opel's image and reputation since taking the helm in March 2013, resigned this week making way for finance chief Michael Lohscheller to become the next CEO of the 155-year-old carmaker.
German-based Opel will be pressed by its new owners PSA to draw up a plan to return to profit once the acquisition, agreed in March valuing the GM division at 2.2 billion euros ($2.46 billion), closes later this year.
"Under Neumann's leadership we have made enormous progress in turning around Opel," GM President Dan Ammann said.
Audi chief executive Rupert Stadler has come under fire for his handling of the emissions scandal, a source told Reuters on Sunday, and the Volkswagen Group is reportedly looking at rehiring Neumann to lead the Audi luxury division.
A growing expansion by the Volkswagen Group into electric cars and digital services as part of a post-dieselgate strategic shift could be another reason to join for Neumann, a trained electronic engineer, analysts said.
PSA, which includes Peugeot, Citroen and DS, wants Opel to return to lasting profit by no later than 2020, with operating margin goals of two percent that year and even around six percent by 2026. This target was never achieved under Neumann, whose push for profitability was hampered by a weak Russian market and effects of Britain's Brexit decision.
"We will vigorously proceed along the agreed path and gain more clout as part of the PSA group," Lohscheller said.
Germany's Frankfurter Allgemeine Sonntagszeitung reported on Saturday that while Neumann views the sale to PSA as the right strategic step, he is concerned that the new owner is underestimating the growing importance of electric cars.
PSA only came eighth in a top-ten ranking compiled by London-based analyst Evercore ISI of carmakers based on average R&D spending between 2014-2016, lagging rivals such as Ford, Renault and leader Volkswagen where Neumann was formerly in charge of group-wide electronics research.
Neumann said on Twitter he will stay as member of Opel's management board until the closing of the acquisition by PSA.
When he lost his post as head of VW's vast operations in China in 2012, sources at the carmaker said at the time he was too aspiring for the then-CEO Martin Winterkorn.