Caretaker coach John Morris is considered the front-runner to land the top job as the club prepares to announce their decision over the next week or so.
Ennis, a 2016 premiership Shark under Flanagan, believes Griffin and former Cowboys and Titans coach Neil Henry are the ideal candidates.
“I would probably lean towards Anthony Griffin to be honest,” Ennis told Fox Sports.
“Only for the sheer fact that he was doing a tremendous job at Penrith last year. They were in the top four for the majority of the season before he got the sack.
“You put someone with a bit of youth and enthusiasm next to him as an assistant and they could do some damage with this roster.”
Ennis said Cronulla’s ideal coach needed to be authoritative and bold with strong leadership skills.
“I’ve been really strong on this – that this playing group at Cronulla needs an experienced coach,” he continued.
“They need someone who is an instructor, who is also a dictator, and has that really good balance of being able to listen to the playing group but being able to put his authority on the group.”