I've seen corporate IT environments with memory and CPU utilization highly under utilized. People tend to order a lot more compute power than they need because of the bureaucracy involved with getting it from another department and getting it setup. Where I was before it took at least 6 weeks to get a VM, months if you had any decent sized disk requirements.
Do a proof of concept with your top talent Linux admins to see if there are apps they can reasonably fit into containers running Linux. You may find that the server footprint to actually run things is much smaller. Start with something easy they would recommend to put on Linux w/o development time.
There are probably cyclical applications in the environment that go under heavy load at certain times but then are mostly idle other times of the year (e.g. financial apps at quarter/year end). Prime candidates for this type of thing. If you can get some container orchestration framework running, it will make scaling apps up/down easier.
Through a POC you may find a business case that will save the company some money, or you may find it is a wash. Right now you're at a point where you don't know if there is an opportunity there. Worst case is your top talent Linux admins get to have a fun project to work on.
