What is a 'nearly quotation' called?

Solution 1:

It's a paraphrase:

NOUN

A rewording of something written or spoken by someone else.

EXAMPLE SENTENCES

In his early years as a teacher he wrote explanatory paraphrases of many of Aristotle's works, setting a pattern of exegesis which continued to be followed throughout the Middle Ages.

He cannot get around that by saying he wrote a paraphrase down on a piece of paper.

The interviews were taped, transcribed, and translated: the texts should be considered as paraphrases.

(Definition and examples from Oxforddictionaries.com)

Solution 2:

allusion comes to mind:

an expression designed to call something to mind without mentioning it explicitly; an indirect or passing reference.

So does paraphrase:

A rewording of something written or spoken by someone else.

This also brings to mind how often the suffix esque can be used to accomplish the same. For example, see the Shermanesque statement.

For clarity, esque means:

(forming adjectives) in the style of; resembling.