Once a friend of mine was eating a 美味しそうハンバーガー。 Then I said 味は良さそうなぁ。かじりたいんだ He replied こいつかじりましい？
I wonder what he meant by that. I might have heard wrongly,though. I think it means "does it look biteable" or something...
This phrase does not make sense. I think your friend might have said like:
こいつかじります？ Do you bite this? or Do you want to bite this?
The reason I guess like this is because: The sound of "u" in [す]｛su｝ pronounced by Japanese people is like "i い" sound, because we Japanese pronounce it softer without straining the muscle around the mouth compared to that pronouced by such as a native English speaker in US. If so, you could have heard it like:
こいつかじりま-C？ for こいつかじります？
This phrase does not make sense. I think your friend might have said jokingly like:
"Bite this one, please!" or "Give a bite at this one, please!"
I assume here that the friend is a man.
The reason I guess like this is because:
Generally, "齧｛かじ｝る to bite or to gnaw" is used when animals, especially small animals, eat fruits partially and the like, but it is not used when people eat something. However, because you are non-native Japanese, you might use a word "かじる" without any joke, he interpreted that you jokingly said "かじらせて" instead of saying "一口食べさせて Let me bite just a little bit". So, he replied with a joke using the same word "かじる" as you used.
Specifically, in order to keep the feelings of your joke, he answered with enlonging the last vowel like, "かじりませ～！" with the meaning of "Bite just a little bit!" Certainly the given phrase has a question mark as "かじりませしい？" However, it might be your misunderstanding that you took his reply as a question. In truth, I think that he enlonged or duplicated the last vowel of the phrase while raising the tune to the end like "かじりませえ⤴！"
And it is similar to what I said in the first answer, the Japanese does not pronounce vowels strongly by straining the muscles around the mouth compared to native English speakers, so "え" sound spoken by the Japanese is close to "い" sound by native English speakers. Therefore, even he pronounced "かじりませえ⤴", it could be heard like "かじりましい⤴" by non-native Japanese.