Perhaps one can assume from TSFS that the Mutara Sector was relatively close to Klingon territory, given that Kruge was able to get to it without being challenged, but we don't know how far that was from Ceti Alpha.
This is what I'm basing it on. Also recall Chekov's line in TWOK, that Reliant
was en route to Regula One and would "be there in three days." Kirk later remarks that Enterprise
is "the only ship in the quadrant" when discussing the mission with Spock. Now, quadrant was often used in place of sector in TOS, so maybe that's what he meant. In any case, if Reliant
could reach Regula in a matter of days, it couldn't have been that far from Klingon space.