In my mind, it really depends on how much you value money. Personally, being in secure employment in a place that I truly enjoy working is more valuable than a modest salary increase. You likely spend almost half of your waking adult life going to work and so if a job makes you happy then you cannot put a price tag on that. As an anecdote, a couple of years ago I took a very large pay cut moving to a new job simply because I was miserable in my higher-paid job. I worked hard and over those two years I became a key member of the team and was rewarded accordingly. Even if I hadn't had a pay rise, I'd still be infinitely happier than I was before; I no longer wake up in the morning and think "oh hell, I have to go to work today", which is an incredibly valuable thing to me.
However, if it's a substantial increase in pay or if you really need the extra to make ends meet, then there's plenty to suggest you consider the new offer. But in this situation there's nothing to stop you, should you be offered the job, to speak to your current employer and let them know that you love your current position but cannot afford to turn down the higher salary. Worst case scenario they'll be sorry to see you go and wish you well; best case they might increase your pay and/or benefits if they are keen to keep you on board. Either way, you've shown that you appreciate the environment you're currently in.
I'd say you should check out the details of the new position, go for an interview and do a little research on how they operate to help you decide if it's somewhere you'd be as happy or happier than you are now (and whether or not the pay increase will add to that happiness!). It never hurts to get more interview experience and, should they offer you the job and you decline, you've made a new contact that may keep you in mind wherever they end up in their future career.