You can pretty much copy and paste the explanation from the Chris Antonetti section here except that Chernoff at least seems more likely to entertain the job since it would give him sole authority instead of continuing to work under Antonetti. Of note here is that the Guardians have seemed uniquely good at identifying and developing pitching which could make Chernoff appealing to Boston. He shouldn't be the preference of fans, though, as his selection could mean that ownership wants the team to continue to operate with a slimmed down payroll going forward.
Twins general manager Thad Levine is an interesting one. He is certainly used to operating under payroll constraints in Minnesota, but he also hasn't been afraid to try and be aggressive in free agency when certain opportunities presented themselve including signing Carlos Correa. The Twins seem to have a decent thing going right now, though, and Levine has actively avoided interviews with big market teams in the past.
Jon Daniels' time running the Texas Rangers was a rollercoaster. He is an aggressive executive with a lot of experience running a front office and built some really good Rangers rosters, but the back third of his tenure in Texas was pretty disappointing. It isn't a coincidence that Texas is doing well with a roster that was largely put together by Daniels, but it is unclear if he would be a great fit for Boston especially if the powers that be try to rein him in and keep him from diving into the deep end of the free agent pool constantly.
The top internal option the Red Sox have to replace Chaim Bloom is Brian O'Halloran. Ownership seems to like him well enough and he has a lot of experience and knowledge of the organization. If he does well in the interim role, he could very well become a leading candidate. However, it would be pretty disappointing to go with him instead of getting a new voice with new ideas in the front office.