The outspoken owner blasted Savea following Toulon's 19-10 loss to Agen in the French Top 14 competition on the weekend.
Boudjellal told French radio RMC that Savea has been released and is "free to do what he wants" despite the former All Black having a year remaining on his contract.
"I'm going to ask for a DNA test. They must have swapped him on the plane [when he joined from Hurricanes]. If I were him I would apologise and go back to my home country.
"I've told him that he was free to go and wasn't welcome at Toulon anymore," said Boudjellal
The 28-year-old is in his first Top 14 season, shifting to Toulon after the Hurricanes' 2018 Super Rugby campaign. Savea has largely struggled for form since landing in France, and has played much of his rugby out of position at 12.
Several of Savea's former All Blacks teammates have come out in support of him, among them Barrett who says players are entitled to better support.
"You'd hope so especially for their own players. It certainly doesn't happen here," said Barrett.
"I am supporting Jules and wish him all the best. He's a great player and I am sure he will bounce back in no time."
Savea's mid-season leave to attend his brother's wedding in December caused backlash from Toulon fans.
Savea responded to Boudjellal's comments on Twitter - saying he'll still turn up to training regardless of his boss' stance.
And Savea received support from former French Top 14 and international rugby stars Bryan Habana and Thierry Dusautoir.
Since his debut for the Hurricanes in 2011, Savea played 116 times for the franchise, scoring 45 tries and winning the title in 2016.
He played 54 times for the All Blacks from 2012 to 2017, scoring 46 tries and winning the Rugby World Cup title in 2015.
Last month it was announced fellow former All Black Malakai Fekitoa will leave Toulon at the end of the season to join London Wasps.
Toulon are 11th in the French Top 14 standings.