diff --git a/hgext/lfs/wrapper.py b/hgext/lfs/wrapper.py
--- a/hgext/lfs/wrapper.py
+++ b/hgext/lfs/wrapper.py
@@ -236,6 +236,10 @@
         # the revlog.
         if rl.opener.lfslocalblobstore.has(metadata.oid()):
             skipflags &= ~revlog.REVIDX_EXTSTORED
+        elif skipflags & revlog.REVIDX_EXTSTORED:
+            # The wrapped method will set `skipread`, but there's enough local
+            # info to check renames.
+            state[b'safe_renamed'].add(node)
 
     orig(rl, skipflags, state, node)
 
diff --git a/mercurial/interfaces/repository.py b/mercurial/interfaces/repository.py
--- a/mercurial/interfaces/repository.py
+++ b/mercurial/interfaces/repository.py
@@ -878,7 +878,9 @@
 
         If individual revisions cannot have their revision content resolved,
         the method is expected to set the ``skipread`` key to a set of nodes
-        that encountered problems.
+        that encountered problems.  If set, the method can also add the node(s)
+        to ``safe_renamed`` in order to indicate nodes that may perform the
+        rename checks with currently accessible data.
 
         The method yields objects conforming to the ``iverifyproblem``
         interface.
diff --git a/mercurial/revlog.py b/mercurial/revlog.py
--- a/mercurial/revlog.py
+++ b/mercurial/revlog.py
@@ -2874,6 +2874,7 @@
             )
 
         state[b'skipread'] = set()
+        state[b'safe_renamed'] = set()
 
         for rev in self:
             node = self.node(rev)
diff --git a/mercurial/verify.py b/mercurial/verify.py
--- a/mercurial/verify.py
+++ b/mercurial/verify.py
@@ -529,6 +529,8 @@
             else:
                 # Guard against implementations not setting this.
                 state[b'skipread'] = set()
+                state[b'safe_renamed'] = set()
+
                 for problem in fl.verifyintegrity(state):
                     if problem.node is not None:
                         linkrev = fl.linkrev(fl.rev(problem.node))
@@ -560,7 +562,7 @@
                     else:
                         del filenodes[f][n]
 
-                if n in state[b'skipread']:
+                if n in state[b'skipread'] and n not in state[b'safe_renamed']:
                     continue
 
                 # check renames
diff --git a/tests/test-lfs.t b/tests/test-lfs.t
--- a/tests/test-lfs.t
+++ b/tests/test-lfs.t
@@ -218,6 +218,15 @@
   R large
   $ hg commit -m 'renames'
 
+  $ hg cat -r . l -T '{rawdata}\n'
+  version https://git-lfs.github.com/spec/v1
+  oid sha256:66100b384bf761271b407d79fc30cdd0554f3b2c5d944836e936d584b88ce88e
+  size 39
+  x-hg-copy large
+  x-hg-copyrev 2c531e0992ff3107c511b53cb82a91b6436de8b2
+  x-is-binary 0
+  
+
   $ hg files -r . 'set:copied()'
   l
   s
@@ -796,27 +805,57 @@
   $ test -f fromcorrupt/.hg/store/lfs/objects/66/100b384bf761271b407d79fc30cdd0554f3b2c5d944836e936d584b88ce88e
   [1]
 
-Verify will not try to download lfs blobs, if told not to process lfs content
+Verify will not try to download lfs blobs, if told not to process lfs content.
+The extension makes sure that the filelog.renamed() path is taken on a missing
+blob, and the output shows that it isn't fetched.
 
-  $ hg -R fromcorrupt --config lfs.usercache=emptycache verify -v --no-lfs
+  $ cat > $TESTTMP/lfsrename.py <<EOF
+  > from mercurial import (
+  >     exthelper,
+  > )
+  > 
+  > from hgext.lfs import (
+  >     pointer,
+  >     wrapper,
+  > )
+  > 
+  > eh = exthelper.exthelper()
+  > uisetup = eh.finaluisetup
+  > 
+  > @eh.wrapfunction(wrapper, b'filelogrenamed')
+  > def filelogrenamed(orig, orig1, self, node):
+  >     ret = orig(orig1, self, node)
+  >     if wrapper._islfs(self._revlog, node) and ret:
+  >         rawtext = self._revlog.rawdata(node)
+  >         metadata = pointer.deserialize(rawtext)
+  >         print('lfs blob %s renamed %s -> %s'
+  >               % (metadata[b'oid'], ret[0], self._revlog.filename))
+  >     return ret
+  > EOF
+
+  $ hg -R fromcorrupt --config lfs.usercache=emptycache verify -v --no-lfs \
+  >                   --config extensions.x=$TESTTMP/lfsrename.py
   repository uses revlog format 1
   checking changesets
   checking manifests
   crosschecking files in changesets and manifests
   checking files
   lfs: found 22f66a3fc0b9bf3f012c814303995ec07099b3a9ce02a7af84b5970811074a3b in the local lfs store
+  lfs blob sha256:66100b384bf761271b407d79fc30cdd0554f3b2c5d944836e936d584b88ce88e renamed large -> l
   checked 5 changesets with 10 changes to 4 files
 
 Verify will not try to download lfs blobs, if told not to by the config option
 
   $ hg -R fromcorrupt --config lfs.usercache=emptycache verify -v \
-  >                   --config verify.skipflags=8192
+  >                   --config verify.skipflags=8192 \
+  >                   --config extensions.x=$TESTTMP/lfsrename.py
   repository uses revlog format 1
   checking changesets
   checking manifests
   crosschecking files in changesets and manifests
   checking files
   lfs: found 22f66a3fc0b9bf3f012c814303995ec07099b3a9ce02a7af84b5970811074a3b in the local lfs store
+  lfs blob sha256:66100b384bf761271b407d79fc30cdd0554f3b2c5d944836e936d584b88ce88e renamed large -> l
   checked 5 changesets with 10 changes to 4 files
 
 Verify will copy/link all lfs objects into the local store that aren't already