The 31-year-old has endured a turbulent few months during which he angered staff and fans at West Brom by attempting to engineer a move to QPR on deadline day in January.
He also missed out on Nigeria's African Cup of Nations win after falling out with coach Stephen Keshi.
And former Super Eagles coach Samson Siasia, who coached the Nigeria Under-23s to a silver medal in the 2008 Olympics where Odemwingie was the overage player, retains doubts about the player.
"Would I invite Odemwingie to the national team if I was the head coach at the moment? No I wouldn't," said Siasia, who was in charge of the senior Nigeria team from 2010 to 2011.
"We need players that will steer the upcoming ones in the right path and act as role models. If he does not do that, he will only end up destroying the team."
Speaking to supersport.com, Siasia added: "He confuses me to be honest.
"On the pitch he's a great player that every coach would want in his team, but off it he's a loose cannon.
"He needs to calm down and understand he now has a wife and a kid who look up to him as an example.
"I pray he matures quickly because Nigerians will want to see him back in the national team."
Odemwingie has made just five substitute appearances for West Brom since the closure of the January transfer window.