Avram Grant left Fratton Park last week after a turbulent off-field spell at the club, which has seen Portsmouth drop into the Championship after a nine-point penalty for entering administration.
Andronikou says there has been a lot of interest in the job, despite the unsecure position of Pompey.
"We've had half a dozen come forward so far," he told the Portsmouth News.
"Brendan Rodgers is a name that has been recommended to us by a third party. He is definitely in and around our thoughts.
"Steve Cotterill is another one of the names that seems to have interest in Portsmouth, we've also been told about him."