Gregorius seems unlikely to accept a qualifying offer. He just played on a one-year deal and had a strong season that merits a four-year contract in the vicinity of $14-16M annually. It’s unknown whether that offer will materialize in this uncertain free-agent period, with MLB’s 30 teams losing a combined $3 billion because of the pandemic. That uncertainty could make accepting the qualifying offer more reasonable to Gregorius, but it still might not be enough.
A major consideration in his decision will have to be next year’s shortstop class, which is loaded with Corey Seager, Trevor Story, Francisco Lindor, Carlos Correa and Javier Baez. Gregorius is a distant sixth in that group. This offseason, he and Marcus Semien are the top two free-agent shortstops.
I think you have to make the QO, it's win-win. Either he takes it and you have him for a year and then can pursue one of those other guys if necessary, or he doesn't and you find some other one-year bridge to that free agent class (again, if necessary). If you haven't been able to keep JT those SS free agents will be even more of a factor. But actually signing Didi to a three-year deal is a distant third or even fourth of the possible options.
Lindor's probably available in trade right now but Phils have neither the depth, nor it seems, the money to extend him quickly. But again, if JT gets away....