The phrase "eager to seek" is grammatically correct and can be used in written English.
It indicates a strong desire or enthusiasm to pursue or look for something. Example: Sarah was always eager to seek new challenges, which is why she decided to start her own business.
He is forward-looking and eager to seek information and ideas elsewhere.
Looking ahead to bigger majorities in January, congressional Democrats have been less than eager to seek compromise.
Mr. Vomvolakis said his client was once in denial of his mental illness, but now accepted that he has problems and was eager to seek treatment.
Executives close to Cable and Wireless said today that the parent company was eager to seek a "local solution" to the sale of its Hong Kong subsidiary.
I don't know Muñoz's music, but Shaffer describes it so vividly, and so affectionately, that I am eager to seek it out.
Surprisingly, perhaps, it is Conservative MPs rather than Liberal Democrats on the Government side who have been most alarmed by the Prime Minister's bellicosity, and most eager to seek clarification.
He now walks around like he is the Mayor, shaking hands, seeking out conversations and eager to try new experiences.
It is evident that Governor Jeb Bush, then seeking re-election, was eager to see Wuornos despatched into the hereafter with as little fuss and as much publicity as possible.
Eager tourists are arriving to seek out shabby chic amid the phosphorescence of decay.
A recent move to restrict textile imports from China shows that the Bush administration is still eager to dabble in protectionism to seek political gain, but a retreat on steel tariffs would help avoid an escalation in global trade tensions.
James, the eager mollifier, was too ready to seek refuge in convoluted references to "distinguished outside learned counsel" mixed with patronising explanations for the plebs on how large corporations delegate small details like paying off villains.
