Can I avoid capital gains on the sale of a rental property by putting the gains into an existing rental property? (e.g. pay off mortgage, repairs, etc.)?

I have multiple rental properties, all with mortgages. I know I've seen articles saying if I sell a rental I can avoid capital gains by purchasing a new rental property. 

But what about existing ones? Can I avoid capital gains by taking the 'gain' amount and say putting it towards the mortgage of one or more existing rental properties?  I've not found any mention of that anywhere.