Strachan has held talks with Pompey chairman Milan Mandaric about the possibility of replacing Harry Redknapp in the hot seat at Fratton Park but he felt that at this moment in time he didn't want a return to club management.
"I had a cup of coffee in London with Gordon to discuss the matter," Portsmouth Director Terry Brady has told his clubs official website.
"Gordon has come to the conclusion at this part of his career that the timing is not right and he can't force himself to make the move from Southampton to Pompey so soon after leaving St Mary's.
"Therefore negotiations will not be concluded but Gordon nevertheless thinks this is a fantastic club with a wonderful atmosphere and he has the greatest respect for both.
"Furthermore he thanks the club for the constructive discussions and he wishes Portsmouth Football Club well in the future."