Looking on the internet deeply has found these results:

extensive interest is the most popular phrase on the web.

deep interest 1120,000 results on the web	extensive interest 1132,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
Nov 12, 2015 ... Man arrested in University of Missouri threats had 'deep interest' in ... shoot black University of Missouri students expressed a "deep interest" in�... Feb 5, 2009 ... Also, your title says "a deep interest for" and in your post you say "deep interest in ". Which are you asking about? (You might want to edit your�... Nov 12, 2015 ... Missouri man arrested for threats against Mizzou students had 'deep interest' in Oregon shooter � By Jen Hayden. Thursday Nov 12, 2015�... The words by the other commenters are all good. Generally, "deep interest" is good enough because saving a word or two like that ultimately is no saving at all.	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

deep interest

1120,000 results on the web

extensive interest

1132,000 results on the web

More popular!

Nov 12, 2015 ... Man arrested in University of Missouri threats had 'deep interest' in ... shoot black University of Missouri students expressed a "deep interest" in�...
Feb 5, 2009 ... Also, your title says "a deep interest for" and in your post you say "deep interest in ". Which are you asking about? (You might want to edit your�...
Nov 12, 2015 ... Missouri man arrested for threats against Mizzou students had 'deep interest' in Oregon shooter � By Jen Hayden. Thursday Nov 12, 2015�...
The words by the other commenters are all good. Generally, "deep interest" is good enough because saving a word or two like that ultimately is no saving at all.

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.