The phrase "anxious to pick" is correct and usable in written English.
It can be used when expressing eagerness or a strong desire to choose or select something.
Example: "She was anxious to pick her favorite dress for the upcoming event."
Alternatives: "eager to choose" or "keen to select".
Nor was Ms. Kolody anxious to pick out one of the discounted thermal sweaters piled near the cash registers.
Commercial banks regarded Freddie Mac and Fannie Mae as competitors and were anxious to pick up business that would result from scaling back the two companies.
For others, the capture seemed unremarkable because, as Mrs. Peterson, the mother of Davin Peterson, noted, "I'm glad, but there are so many others in Al Qaeda who are anxious to pick up where he stopped".
Villas-Boas will find himself caught between the devil and the deep blue sea tonight, as he'll surely be anxious to pick a team that's strong enough to see off tonight's Slovenian opposition, but not so strong that he'll need to use key players he might prefer to rest ahead of Sunday's match against the Premier League champions.
If people really understand what an enormity it is to take even one human life, even when justified in self defense, they'd be less anxious to pick up guns to promote their interests.
Trump's vehemence poses an early dilemma for Republicans who are deeply suspicious of Putin but are anxious to avoid picking a fight with Trump even before his inauguration.
The war of Texan independence involved much daring, but was also explicitly motivated by the desire to escape Mexico's laws against slavery: Anglo settlers were anxious to import black slaves to pick cotton.
Just a day earlier I'd been racing along the New York State Thruway at 70 m.p.h., anxious not to be late to pick up the canal boat.
She leaves, in a hurry, anxious to be back in time to pick up her son from nursery.
The vines, bright green and jaunty, marched in rows up the hillside, but September is always an anxious month, since winemakers must choose the perfect time to pick.
