There is an authentic hadeeth where the Prophet salla Allahu alaihi wa sallam told us that if the Athan is being called while one of you is holding his drink, let him not put down the glass and let him finish his drink until he is satisfied.
This hadeeth is reported by Al Hakem in AL Mostadrak, if I am not wrong.
This hadeeth is only regarding a person drinking and not eating. Therefore, if the Athan calls and one is chewing food, it is OK to finish what is in his mouth but he must not eat any more.
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And Allah knows best