From Longman Dictionary of Contemporary Englishdeep in thought/conversation etcdeep in thought/conversation etcNOTICE#thinking so hard or paying attention to something so much that you do not notice anything else that is happening around you → deep
Examples from the Corpus
deep in thought/conversation etc• Clarence and the mayor were still deep in conversation.• The boy-him, he had to remind himself-looked deep in thought.• Anthea and the professor had been deep in conversation with an eager group of ladies from Leicester, leaving Meryl momentarily alone.• He was deep in conversation with the daughter of the house, a little girl of about twelve.• The Count was deep in conversation with the mayor, who was staring down at his feet. 