Since Burrow has had a year-long injury already in the past, I can't imagine he would go into this season with the possibility of putting hundreds of millions of dollars in jeopardy.
If he were to rupture an achilles week 1, then they likely wouldn't give him an extension this season at all, or perhaps even before next year (and make him show he recovered well first by playing at a high level next season). Then they could also tag him the year after that. It's just way too risky and too much at stake for any agent in their right mind to risk (2% agent fee of a 300 million contract, is an easy 6 million bucks).
I would place the likelihood of a deal by Friday at 90% and would be SHOCKED if there is no deal in place.