Bogaerts hired Scott Boras to represent him, knowing full well that Boras' primary tactics are to get to free agency and then ask for lots and lots of money. That's how Boras operates. I know it. You know it. And certainly Bogaerts knows it. I do not think any of us knows Bogaerts well enough to know where money falls on his list, but we do know he hired Boras to be his agent, so it is certainly a priority for him on some level. If Bogaerts had any interest in a cheaper deal, there would have been no need for the opt out clause, which was absolutely not put in there so that he could take less money instead of reaching free agency at age 29.
If Bogaerts extends, it will be or money similar to what Correa/Seager/Baez/etc. will be getting this off-season. And all of them will be benchmarking something in the neighborhood of Francisco Lindor's extension (10 years $341mill). They won't all get it, and maybe none will, but that will be the starting point.
The most likely bargain of the bunch is probably Baez, who is the same age as Bogaerts and started the season off struggling heavily (although he has been flat out thumping since being dealt). But his right-handed pop bat would play well in Fenway and he does bring extremely strong defensive play that you just don't get from Bogaerts...