The meeting took place at the private residence of the Rivers governor in Port Harcourt, the state capital.
Obi was a member of the Peoples Democratic Party (PDP) until May when he defected to the Labour Party to pursue his presidential ambition.
Wike was one of the presidential hopefuls of the PDP, but he placed second in the primaries, losing to Atiku Abubakar who emerged as the party’s standard-bearer.
The Rivers governor was also overlooked for the vice-presidential candidate position, with Atiku opting for Ifeanyi Okowa, Delta state governor.
Wike has not publicly commented on missing out on becoming the running mate of Atiku.
Obi’s visit to Wike comes a few days after David Umahi, the Ebonyi governor who is an All Progressives Congress (APC) member, had met with the Rivers governor.