"to gauge their interest" is correct and usable in written English. You can use it to indicate that you are trying to measure how interested someone is in a particular thing. For example, "I asked my friends questions about the new project to gauge their interest in participating."
The students also started getting in touch with friends and acquaintances on campus to gauge their interest.
Tudge told the ABC last month he was consulting different regions to gauge their interest in the card.
When he came back in May and lost his first three starts, the A's called the Yankees to gauge their interest in him.
Eventually, the studio agreed to a purchase price of $3.5 million and sent the phone book to Mel Gibson and Julia Roberts to gauge their interest.
Dr. Tepper would not reveal the amount subjects are paid -- it's small, she said -- because she wants to gauge their interest in taking part in research.
ELS representatives originally contacted state officials to get a list of recent job applicants whom they could contact to gauge their interest in employment with the company.
… I polled the class to gauge their interests and confirmed that many of the students were interested in pursuing careers in a medical or health-related field.
At the start of the semester I polled the class to gauge their interests and confirmed that many of the students were interested in pursuing careers in a medical or health-related field.
The biggest national donors were the subject of entire dossiers, as fund-raisers tried to gauge their interests, annoyances and passions".
[Extract from reflective journal] I was struck by the balancing act that I had been observing – by the coder's clear sense that she was serving both patient and doctor and always trying to gauge their interests.
An extract from DS' reflective journal written just after this observation read: I was struck by the balancing act that I had been observing – by the coder's clear sense that she was serving both patient and doctor and always trying to gauge their interests.
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.