The former Super Eagles striker has questioned the decision to keep William Troost-Ekong as captain after the defender left European football for Saudi Arabia in 2024.
Troost-Ekong joined Al-Kholood from Greek side PAOK but continued to lead Nigeria under former coach Finidi George and later Eric Chelle. He has since retired from international football.
For Odemwingie, however, the captaincy should have changed as soon as the experienced defender moved away from European football.
Speaking on Brila FM with former Nigeria international Ifeanyi Udeze, as reported by Soccernet.ng, Odemwingie argued that leadership of the Super Eagles should reflect the standards expected from the country's leading players.
"It got to a point that when I see players like William Troost-Ekong, our captain (now retired), he moved to Saudi Arabia, and he was still captain of the national team," Odemwingie said.
"I understand that he's still riding on his past glory, but, for me, when things like that happen, it's an automatic out for captaincy."
The former West Bromwich Albion forward believes playing in a top European league should be an important requirement for anyone considered for the Super Eagles armband.
"Any player that doesn't play in a top league shouldn't captain the Super Eagles, it's a fact. It's not natural. Not just Nigeria, but any country," he added.
Odemwingie also drew a distinction between moving to Saudi Arabia and playing in Turkey, where Victor Osimhen currently represents Galatasaray.
He pointed out that Galatasaray compete in the Champions League, making Osimhen's situation different from players who leave European football altogether.
According to Odemwingie, the pursuit of elite European competition demonstrates that a player remains focused on the highest level.
Odemwingie's comments come as Nigeria have already moved on from Troost-Ekong's leadership, with Wilfred Ndidi now wearing the Super Eagles captain's armband.
The Besiktas midfielder fits Odemwingie's criteria of a player competing in European football, while Moses Simon, Victor Osimhen and Alex Iwobi have also served as vice-captains.