This is incorrect. As people save more and consume less, interest rates get lower and lower. In fact, since people don't have to pay interest, they get to save more and more as the bank gets less and less of their money. Japan and Germany have the lowest interest rates and aren't known for saving less.

Also, liquidity preference predicts that people will save an unlimited amount of money at 0% interest if they have sufficient income that exceeds how much they intend to spend.