Lately, it seems that certain fans have been insisting that TOS absolutely took place in the 22nd century, but within the series, there isn't actually a solid basis for that.
I think there have always been some who favored that interpretation.
To summarize:
"Tomorrow is Yesterday" and "Space Seed" suggest late 22nd century.
"Miri" and "Metamorphosis" suggest 23rd century.
"The Squire of Gothos" suggests 28th century.
Blish "Miri" suggests 27th century. Blish "Squire" suggests 28th century. Blish "Space Seed" explicitly states 23rd century.
The Making of Star Trek says 23rd century.
TAS: "The Infinite Vulcan" aligns with "Space Seed" in suggesting late 22nd or early 23rd century -- Keniclius is from the Eugenics Wars era, would "have to be over 250 years old," and has been out of touch for 200 years. But "The Slaver Weapon" says the
last of the four Man-Kzin Wars was 200 years before, suggesting late 23rd century at the very least. (In the Known Space universe, the Man-Kzin Wars span the 24th and 25th centuries, and "The Soft Weapon" is in the mid-27th century.)
TMP indicates late 23rd century at earliest. TMP trailers state 23rd century. TWOK opening caption says 23rd century and dialogue suggests post-2283, putting TOS in late 2260s.
TNG says McCoy is 137 in 2364, ruling out a TOS time frame earlier than 2260s.
VGR: "Q2" explicitly dates the end of the 5-year mission as 2270.
