Flanagan could be rubbed out for communicating with the club during his 12-month ban in 2014, and despite having the club's backing, Cronilla are making plans to replace him should be face suspension.
Barrett, who is currently on leave after being replaced by Des Hasler at Manly, tops the Sharks' wish list of coaching candidates and is considered the favourite to land the job should it become available. Other names on Cronulla's radar include St Helens coach Justin Holbrook and former Dragons mentor Steve Price.
Former premiership Shark Luke Lewis has tipped assistant coach John Morris to take over the reigns from Flanagan if he is forced out of the club.
"He knows the game like the back of his hand, he's very smart and he knows the boys really well,'' Lewis told the Herald.
"He also has a good working relationship with Jim Dymock.
"He's ready for it. He's been in the Under-20s system, he's been in the first-grade system, he's played first grade, he knows what it takes to be at your best, he loves footy and understands the boys.
"If the opportunity came he's take it with both hands and shine."
An investigation into the Sharks' salary cap scandal found evidence of Flanagan contacting the club over issues such as recruitment and player retention.
Cronulla chief executive was not willing to speculate on the coaching situation.
“What I can say is that Shane Flanagan is our coach, he is contracted for 2019, he’s done a wonderful job and he will continue to coach the team,” Russell told the Herald.
“It will be training and business as usual for us.