Parker returned to South Africa this year following an unsuccessful spell with Dutch outfit FC Twente, and he was quickly snapped up by Amakhosi towards the end of the pre-season.
The Bafana Bafana hitman marked his Chiefs debut with a goal from the penalty spot, but he admits he still has some work today before he reaches his full potential.
"I was not part of the team's pre-season training because I arrived late [from Holland], so I am still a long way off from full fitness. But I have enjoyed playing for Chiefs and I have been happy since my arrival here," he told Times Live.
Parker has been used to occupying the central striker's role during his footballing career, but Chiefs coach Vladimir Vermezovic has implemented the 25-year-old in a more supporting role behind strike partner Lehlohonolo Majoro.
However, Parker admits that, for now, he is happy to fill any position on the field as he looks to regain his full fitness.
"I am comfortable there (in that position). I am happy feeding Majoro to get the goals for the team because I know that I will soon start scoring as well," he added.