***** NOT A TEACHER *****
(1) Yes, I believe that both sentences are "correct."
(2) I believe that most books tell us that we should say:
(3) I believe that many (most) Americans ignore that rule and
use "likely" by itself, as in your two examples.
(4) I believe that if you are doing university-level writing (or even
speaking), you should follow the rule, though. That is, write:
The Bengals could quite likely get a quick pick.
(5) I was able to find on the Web this discussion:
No. 1. We will likely be finished by December.
No. 2. We likely will be finished by December.
The expert who answered this question said that s/he preferred to
"bury" the adverb inside the verb phrase (as in No. 1). S/he said that
No. 2 was not wrong, of course.
(6) I am sure that you have noticed that No. 1 reads smoothly,
but if you read No. 2 aloud, do you notice that you are "forced" to stop
for a pause after the word "likely"? I guess that some people would say
No. 2 is used when you wish to emphasize the adverb. It is only my
opinion that many Americans probably prefer No. 1.
(7) By the way, "likely" is a so-called sentence adverb. That is, it
refers to the whole sentence. If you use "perfect" English and use
very/most/quite in front of "likely," then you can place it many locations:
Quite likely, the Bengals could get a quick pick.
The Bengals (very) likely could get a quick pick.
The Bengals could (most) likely get a quick pick.
The Bengals could get a quick pick, most likely.
(8) I think that if we just place the adverb after the first auxiliary,
we will be writing "good" English. Later on -- as we understand
English better -- we can move it around to express different
feelings. I am an old man and English is my only language, but
adverb placement still confuses me.
(9) Hopefully, a teacher will soon give us the ("thee")answer.
Student or Learner