According to Sun Sport, the 62-year-old Grant could be announced at the end of the current season as he is expected to have full pre-season training with his players.
Grant is currently in India, where he is coaching Indian Super League outfit North East United FC.
“Grant has worked in Africa before, where he wrote a successful story with Ghana, where he spent three fruitful years. He would come in handy for frustrated Chiefs,” a source told Sun Sport.
Chiefs football manager Bobby Motaung could not confirm that Grant was in the running for the coaching job, saying Chiefs could have an idea on who they are eyeing before the end of the month.
“We’re not in a hurry. This is a process,” he said.
“We are yet to review and assess those applications. The season has not finished yet, hence we are taking it easy.
“We don’t have deadline or set any timelines on when we should appoint a coach. But that will be before the new season starts,” he said.
Luc Eymael of Free State Stars and former Orlando Pirates and Cape Town City coach Eric Tinkler have also been linked with the Chiefs job.
Eymael, however, is said to be finalising his move to SuperSport United, where he will take over next month.