If there is a "phrase of the week", in German would it be correct to call it "die Phrase der Woche" or would it be better to say "die Redewedung der Woche" or "der Ausdruck der Woche"?
I'd avoid "Phrase der Woche" because "Phrase" may have a negative connotation, it's usually used in terms like "hohle Phrase" ("hollow" = meanigless) and people will think along these lines. It evokes marketing jibberish or business bs (no offense!), even if used fairly neutrally.
"Ausdruck der Woche" and "Redewendung der Woche" will work, the former more in a shorter sense like "word of the week", the latter in more fixed sense like "proverb of the week". I'd personally go for "Ausdruck der Woche".
I agree with Stephie: "Phrase" has a negative connotation, the first thing I thought of was "Phrasendrescher - some one who uses meaningless standard phrases.
It depends in what context you'd like to use it, my suggestion would be
Spruch der Woche
This works well for eg something funny or curious - not so much for "serious" topics like language.
I agree with Stephi too but would like to add another Term: Motto - so "Motto der Woche" would be an adequate translation.
"Spruch der Woche" is not bad but "Spruch" may also sound blatant and is sometimes associated with empty promises.
"Ausdruck der Woche" or "Redewendung der Woche" - as proposed by Stephi - is quite cumbersome and not really to be found in spoken language.
Even more: "Ausdruck der Woche" or "Redewendung der Woche" could be used in a newsletter for writers where linguistic matters are discussed.
My proposal "Motto der Woche" is a phrase that could be used by your boss on Monday meetings in order to motivate staff (>>e.g. Selling, Service, Satisfaction<<). And a family could also have a "Motto der Woche" as >>The garden needs our help<< in order to remind all members of the family to do something about the mess in the garden and by the end of the week the family aims to have a nice garden again.