The phrase "are necessarily looking for" is correct and usable in written English.
It can be used when discussing specific requirements or expectations in a context where something is being sought after.
Example: "In this project, we are necessarily looking for innovative solutions that can address the challenges we face."
Alternatives: "are specifically seeking" or "are explicitly searching for".
I don't think scientists are necessarily looking for popularity in the first place.
"I just don't think that's an item that people are necessarily looking for today".
"I don't think the people of New Jersey are necessarily looking for another slick politician right now," Mr. Marcus said.
"I'm not suggesting they are necessarily looking for it... they can't help but make money".
For example, if you're talking about dating, don't assume that the members of a male audience are necessarily looking for a girlfriend.
But a new series about Mr. Guadagnino was "not a show that we were necessarily looking for," said Chris Linn, MTV's executive vice president for programming.
Specifically, job searching is becoming more passive: people aren't necessarily looking for a new job but are permanently open to their next career move.
Minnie (Bel Powley) electrified audiences in Diary of a Teenage Girl and reaffirmed that young women who are reconciling their relationship with sex aren't necessarily looking for or even in need of a relationship.
"What we've seen, particularly with Russia, is that military applications of cyber are not necessarily looking for a kinetic effect.
Meanwhile, I'm holding down a job, settling in with new roommates and keeping myself open to possibilities -- but, like, super-hot, non-threatening possibilities who aren't necessarily looking for commitment but who also aren't afraid of it.
But people who visit the site rarely aren't necessarily looking for the most recent news; they're more likely looking for the most interesting and engaging updates that have been posted since the last time they logged on.
