Cooper, who played seven times for Pompey during the 2001/2 season, trained with the club on Tuesday following a trial with Torquay.
Whittingham, also hoping to extend Bondz N'Gala's spell at the club, told the Portsmouth News: "We've said before that we think Shaun would add value to the squad.
"We will have to wait and see if that is possible or not.
"The budget is not set. If there is a player and the board think it's possible and if we would like to do it, then there is a possibility."