Winger Selwyn Cobbo is another priority, while fullback Hamiso Tabuai-Fidow's new deal is being worked through now
According to the NRL contract list, the Dolphins have 14 players off contract at the end of 2027 and two yet to re-sign for next season in Ray Stone and Brad Schneider.
Key outside backs Tabuai-Fidow, Cobbo, Farnworth and Bostock are players around whom a premiership side could be built.
Thomas Flegler, Morgan Knowles and Connelly Lemuelu are top line forwards on the list.
The Dolphins are dealing with salary cap machinations each day and Woolf has made the point that while some players may leave decisions on their futures until November 1, when they become free agents, it is not a date to cause anxiety.
Some players will seek to finalise deals sooner and others may wait, particularly with the Dolphins on the cusp of a maiden finals berth.
Clubs, in agreement with players and their management, will often put talks on hold in mid-August to focus on winning a title.
Woolf was asked directly about the club's ability to keep NSW representative Bostock and England international Farnworth amid fears one will have to move on. His answer was enlightening.
"We are very comfortable with the situation and we are very confident we can keep those guys, and that those guys want to be here," he said.
"November 1 puts this date out there that everyone thinks it has got to be done by, but we have got a long time to go until November 1.
"Just because guys go to November 1 doesn't mean they are going elsewhere either. We have got no indication from either of those guys, or any of the guys that are off contract, that they want to go to the open market.
"All of our conversations are about staying and about them being really happy with where they are at and where the club is at.
"We just have to make sure we can come up with something that is attractive and we can make it work."
Cobbo was asked after Saturday's 40-32 win over his former club Brisbane whether he wanted to re-sign.
"Yes," he said.
"I've just got to keep playing good footy and let my manager do all the talking. I've got to do the actions.
"The Dolphins have done a lot for me."
Woolf's thinking is exactly the same.
"We haven't sat down with Selwyn yet but he is a priority and he is someone we are going to sit down with in the very near future," the coach said.
"He has been great at our club. We just had to give him an environment that made him happy and we are really happy with how he is going. He has got plenty of games left for us."
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