Yes, it is possible, but there is no reliable option
1. Steam offline messages / Steam mobile
You can still send your Steam friend a message through the known Steam messaging system. As long as he remains offline, the message will be stored and he will be notified when he then logins again. (This is then a green envelop in his Steam software.)
If he uses Steam mobile (liek for Android), he can also use this messaging system on his phone. So maybe you're lucky and he fetches your message on his phone to answer. But TBH I don't see much friends on my list using Steam mobile.
2. Personal information on his profile
You can open his Steam community profile - if he has one - to see his personal information which he gives access to. If you're lucky, then maybe he is running a personal website for his own, where you can fetch his Email adress. Otherwise there is no option to mail him but per Steam messaging system.
3. Steam and Facebook
(I only have this in German localization, but you'll understand.)
Through Steam community you're also able to connect your Steam profile with your Facebook profile. If your friend did this, you can right-click him in your friends bar and select "Visit Facebook page..." where you get directly redirected to his personal Facebook page. If he did, you're lucky, because once you log in to Facebook, you'll never log out...
You may find a phone number or email adress there, but if he's not out of the 60's, he will know how to use data privacy.