The Bolton manager is debating whether to recall the two international stars for the home game against Everton on Sunday after they were both demoted to the bench in the opening day draw at Aston Villa.
Greece winger Giannakopoulos was the target of an unsuccessful £1million bid from Manchester City while Nigerian playmaker Okocha has been linked with a move to Qatar.
Allardyce said: "Any speculation regarding moves involving Stelios or Jay-Jay does have an effect.
"But they are both of an age where they are wise and mature. I am sure they will give everything they have should I name them in the team."
"The disclosure of the bid on the Saturday morning wasn't the right thing to do," said Big Sam.
"It should not have happened. That is my only dissatisfaction."
On Giannakopoulos' immediate future Allardyce said: "The situation lies with the chairman.
"He has not said anything to me about the lad going anywhere, so he is still one of our players and available for selection."