The Fratton Park outfit are around £60 million in debt, and Gaddafi Jnr - who is the president of the Libyan Football Federation - is allegedly in the midst of discussions with the club's current owner, Ali Al Faraj.
An unnamed source is quoted as saying: “Colonel Gaddafi’s son Saadi first expressed an interest in taking over from Al Faraj at the end of last year.
“That has gathered pace since the Revenue issued their winding-up order and the deal is 95 per cent done.
“Al Faraj is keen to sell because he knows he cannot afford to finance the debts and does not want his reputation in the Middle East to suffer by presiding over a club that goes bankrupt.
“Saadi is a big football fan and loves the thought of owning a Premier League team.”