I would like to work on this.

WIP path - https://chromium-review.googlesource.com/#/c/chromium/src/+/750527/

Thanks for the patch! I've kicked off a trybot dry run on your CL. Once everything looks good, you can select an owner from components/offline_pages/OWNERS and start the review process by clicking the "Start Review" button in gerrit.

uploaded https://chromium-review.googlesource.com/c/chromium/src/+/754245 

Apologies, applied the wrong component in bulk.

xunjieli@, is this a mechanical change or are there behavior changes in the new API?

This particular one seems to be purely mechanical. 
In some cases, the observer implementation needs to be changed slightly (see last section on https://docs.google.com/document/d/1ch22_dRHPQJ9QArFMmWl_UyVpl-EDXA0PdljGh2kDF0/edit#heading=h.mlge0axnxo7)

In short, because offline_pages's ConnectionNotifier is a "constructive" observer, it needs to check type != CONNECTION_NONE. In this case, it already does so, so no additional changes needed besides the mechanical ones.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/8b5991731783550c806e178188f307e04235719d

commit 8b5991731783550c806e178188f307e04235719d
Author: mallikarjun82 <vm.arjun@samsung.com>
Date: Thu Nov 09 08:23:59 2017

Change ConnectionTypeObserver to NetworkChangeObserver

This CL migrates connection_notifier.h to use NetworkChangeObserver.
More details are in the following bug

Bug:  780474 
Change-Id: Ib00250222ed704646fe0150b1aac420a8dd34e4d
Reviewed-on: https://chromium-review.googlesource.com/754245
Commit-Queue: srirama chandra sekhar <srirama.m@samsung.com>
Reviewed-by: Helen Li <xunjieli@chromium.org>
Reviewed-by: Justin DeWitt <dewittj@chromium.org>
Cr-Commit-Position: refs/heads/master@{#515122}
[modify] https://crrev.com/8b5991731783550c806e178188f307e04235719d/AUTHORS
[modify] https://crrev.com/8b5991731783550c806e178188f307e04235719d/components/offline_pages/core/background/connection_notifier.cc
[modify] https://crrev.com/8b5991731783550c806e178188f307e04235719d/components/offline_pages/core/background/connection_notifier.h
[modify] https://crrev.com/8b5991731783550c806e178188f307e04235719d/components/offline_pages/core/background/request_coordinator_unittest.cc

The patch is merged. 
Can some one help to resolve this bug?