UPDATE: We now have good reason to believe that this was made up - so don't be too heartbroken.
File this under interesting things that could have been: Insomniac was apparently offered the chance to reboot Conker in 2014 but turned it down due to the fast turnaround Microsoft wanted.
The info's popped up in an apparently verified Reddit post (make of that what you will) with the source claiming to have been "with MS for several years" and "provid[ing] additional credentials that verify his position."
The key info is that a there was little interest in a Conker reboot for quite some time because "a lot of people thought the style felt really dated, and that the crude humour of it felt too 90s for modern audiences".
However things changed when Microsoft apparently decided to plan a series of old IP reboots for 2016/17:
"That mostly changed around spring of 2014. All of a sudden, I became flooded with emails and design docs for a new Conker game. Basically, MS wanted to reboot Conker, and was shopping around for developers to make the new game. MS wasn't comfortable developing it, and Rare DEFINITELY wasn't making it.
For a while, it really looked like Insomniac would take on the Conker reboot, they were already doing third-party stuff for MS, and they had made a hit platformer series in the past.
However, Insomiac turned MS down too. Apparently MS wanted Conker to hit store shelves by the end of 2015, and Insomiac refused because of the short dev cycle. MS wanted Conker out the door really quickly, because they wanted to reintroduce audiences to a bunch of older IPs that MS were planning on rebooting for 2016-17, like Perfect Dark and Banjo."
The source also adds in a couple of emails discussing the collapse of the project:
It's interesting to note that around the time this was rumoured to be happening Conker did make a cameo at the end of a Project Spark trailer and is still apparently intended as DLC later this year.
Was this originally planned as part of a marketing/awareness push? At the time Project Spark dev Team Dakota's community manager Mike Lescault responded to fans stating, "we're still working out the details of exactly how and when Conker will be available in Project Spark."