"not eager for" is correct and usable in written English.
You can use it to describe someone who is indifferent about something or has a lack of enthusiasm about something. For example: "The students were not eager for the extra credit assignment, so most of them didn't bother to do it."
I'm not eager for godlike status.
Hewitt is not eager for the next innovation to arrive.
We're not eager for the next life because this one is very entertaining.
Like a lot of private clubs, the corporation and its membership are not eager for publicity.
Executives at Fox said privately at the time that the network was not eager for her to continue.
He was not eager for "the navel-gazing and confessionals and self-obsession that goes on with songwriters".
I expect the creators of the new Torchwood ARG aren't eager for the same fate.
The authority isn't eager for a public discussion of what sort of ad might qualify as creating an imminent threat.
But when Maureen became lost coming back from the concession stand, causing my mother to miss the performance of Godfrey, the Old Redhead, she wasn't eager for an encore.
Until recently, Mr. Warshauer said, residents returning home to their rural retreats from high-pressure jobs in Manhattan, or Stamford and Greenwich in nearby Connecticut, might have grumbled about poor cellphone reception in low-lying areas, but they generally weren't eager for anything beyond the town's single cell tower.
And Yankees Manager Joe Torre, mindful of Brown's medical history -- seven stints on the disabled list for various injuries and ailments since April 2000 -- isn't eager for him to chance it either "If it's something that's going to hinder his pitching, we'll give him a couple of extra days and pitch Wang, Torree said.
