It's been tipped that the two will fight at London's O2 Arena in March. Parker is the current WBO heavyweight champion while Joshua holds the WBA and the IBF crowns.
"There's a good chance [Parker's promoter] David Higgins will fly over in the next week to try and close the deal," he exclusively added.
"Sometimes when you're this close you need to get face-to-face and eye-to-eye. Work on it, keep talking, no one goes home until you make the deal.
"There are two perfect fights for AJ - Parker and Deontay Wilder. The Wilder fight is unrealistic because of what they want. The Parker fight is a lot closer."