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 ultralight poncho tent may save your life: http://www.theultralighthiker.com/ultralight-poncho-tent/ & http://www.theultralighthiker.com/poncho-tent-update/
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.
A reader also 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’.