The former Pompey defender has guided the team away from the League Two relegation zone since taking over from the ousted Richie Barker in March.
"I've got plans in my own head in case I am manager of Portsmouth Football Club," he told BBC Sport.
"If they would like me to do it, I said before that it took me two seconds to decide whether to be caretaker manager as I felt that was the right thing to do.
"It will need to take a lot longer than that. There will need to be frank discussions with the board about where the football club is going, the direction they are taking and if we agree then fine, and if we don't then we'll keep talking."
Awford has won all five of his games in charge of Portsmouth.