Is it possible having license manage in Linux and consume the license in FME Desktop/Server in Windows

In short: yes.

FME Desktop can connect to a floating license server regardless of the OS they both run on.

FME Server has it's own internal licensing engine, it does not use an external license server.

See also this question from earlier today: https://knowledge.safe.com/questions/102939/is-possible-to-have-fme-desktop-and-server-in-wind.html

Hi @kfarasan,

You have tagged the question with 'fme desktop 2015.1'. Does this mean that you are wishing to install and license FME Desktop and FME Server 2015.1? If so, then this version of FME Server licenses itself via a floating license. It changed in FME Server 2016 to its own licensing engine.

So, with this in mind, you can install FME Desktop and FME Server on Windows OS and they can both get their respective licenses from FlexLM license manager installed on a Linux OS.

You might want to check out the answers to the question referenced by @david_r above, for things that you might want to consider.

Essentially as long as the machines that FME Desktop and FME Server are installed on can communicate with FlexLM on the Linux machine, you should be fine.

Good call spotting that tag!