What a good idea that would be, especially if you need to use both hands for trekking poles on rough or steep terrain. When the weather is really humid, you really need a roof to keep you dry (and warm). A raincoat in such circumstances will just see you soaked and frozen.
In such circumstances my Pocket Poncho Tent may save your life.
There are several possibilities. For example Antigravity Gear has a model featuring clips which attach your trekking umbrella to your back pack. https://www.antigravitygear.com/shop/rain-gear/swing-handsfree-backpack-umbrella/
There are several other possibilities, such as:
A search for ‘hands free umbrellas’ will provide you with lots of fun and amusement!
One I particularly like is the Ufocap: http://ufocap.tradekorea.com/product/detail/P280367/UFOCAP—Innovative-Umbrella.html?minisiteprodgroupno=32229 These little guys cost about $10 on eBay and weigh about 170 grams. Even if they look a bit silly they should do the job. The ones with transparent panels (at least at the front) would help you see where you were going.
Best of all: A reader recommends this excellent DIY solution to attaching your umbrella to your pack here:https://ramblinghemlock.blogspot.com.au/2014/03/umbrella-rigging.html
I think I would caption this one, ‘Fun with Umbrellas’. Well done ‘Rambling Hemlock’.
You can buy this clamp now if you can’t manage to make your own.