Akpeyi's contract with Chiefs is set to expire in June at the end of the current season with the Nigerian shot-stopper able to sign a pre-contract agreement in January.
Amakhosi are known to yet offer the Super Eagles goalkeeper a new contract.
Other players whose contracts are also set to expire in June and whose future remains uncertain includes Orlando Pirates midfielder, Thabang Monare and SuperSport United striker Thamsanqa Gabuza.
Colombian striker Leonardo Castro and Zambian striker Lazarous Kambole will also see their deals expire at Chiefs.
According to reports in Kwazulu-Natal, Royal AM strikerVictor Letsoalo is headed to an unnamed team in Gauteng next season and could also sign a pre-contract deal with one of the PSL big boys next month while Gabuza could return to Durban.
"It's more than just about money as he wants to fulfil his dream of playing for one of the biggest clubs in the country.
"This is an opportunity for him to go to Johannesburg next season.
Other players that could also move in lucrative deals include SuperSport United duo of Teboho Mokoena, Sipho Mbule and Bongokuhle Hlongwane from Maritzburg United.