The 34-year-old joined the Fratton Park club in 2010 and spent last season playing on a month-by-month deal.
Pompey boss Guy Whittingham was keen to give the Portuguese centre-back a new contract, but Rocha has not agreed terms.
"It would have been fantastic to have added Ricardo to our squad for the new season," Whittingham told the club's official website.
"Myself, the chairman and chief executive have held a series of talks with him over recent months.
"Unfortunately we were unable to finalise a deal, but we wish him all the best for the future.
"Ricardo has served Pompey well over the past few years and it was clear from meeting with him that he still holds a lot of affection for this club."
Meanwhile, the club have confirmed they are temporarily reducing the capacity of Fratton Park to 18,200 due to safety concerns.