Does the Catholic Church quote any saying of Jesus to which His question in John 14:2 can be attributed? In John 14:2 we hear Jesus saying:  "... My Father’s house has many rooms; if that were not so, would I have told you that I am going there to prepare a place for you? " 

I am not able to connect the said words of Jesus to any of His saying in the earlier chapters of John.  In other words,  Jesus does not appear to have promised  his disciples that He would be going to prepare a place for them, prior to His saying at John 14:2, nor is the Evangelist adding a remark from his side explaining that Jesus had said so at such and such time. In fact, John 14 seems to have an abrupt beginning. 

My question is: does the Catholic Church quote any saying of Jesus to which His question to the disciples in John 14:2 can be attributed?
This is not exactly a direct answer to your question, but I don't think there is that much support for translating the verse as a question.  I say this, however, acknowledging that there are translations that are approved by the Roman Catholic and/or Eastern Orthodox Church that show it this way (e.g. RSV, RSVCE, NAB).
The oldest manuscripts were not punctuated, so modern translators have incredible discretion in how they can choose to interpret a verse.  In any case, the way this verse was understood by the Greek Church in antiquity was more along the lines of:

In My Father's house are many abodes; otherwise I would have told you.
I go to prepare a place for you.

(I am using the Orthodox New Testament translation).  There is no question implied.
John Chrysostom (4th century Byzantine), a respected Father of both the eastern and western Church (he is a Doctor of the Roman Catholic Church), clearly understands the verse in the above sense, as he comments:

In My Father's house are many mansions
As He comforteth Peter when bewilderedby saying, &quot;but thou shalt
follow afterwards,&quot; so also He gives this glimpse of hope to the
others. For lest they should think that the promise was given to him
alone, He saith, In My Father's house are many mansions.
If it were not so I would have said to you, I go to prepare a place for you.
That is, &quot;The same place which receiveth Peter shall receive you.&quot; For
a great abundance of dwellings is there, and it may not be said that
they need preparation.
Homily LXXIII on John

This is consistent with how the verse appears in the Clementine Vulgate, and as rendered by the Douay-Rheims translation:

In domo Patris mei mansiones multæ sunt; si quominus dixissem vobis:
quia vado parare vobis locum.
In my Father’s house there are many mansions. If not, I would have told you: because I go to prepare a place for you.

Other sources that I could find in the ANF/NPNF series that discuss or include the entire verse were a translation of the Syriac Diatesseron and Augustine's Tractate LXVIII on the Gospel of John.  Neither of these, from what I can tell from the context, understand the verse as a question. (The aforementioned can both be found online at ccel.org).
The semi-official Greek text of the Eastern Orthodox Church is the 1904 Patriarchal Text, which does not indicate a question:

ἐν τῇ οἰκίᾳ τοῦ πατρός μου μοναὶ πολλαί εἰσιν·  εἰ δὲ μή, εἶπον
ἂν ὑμῖν·  πορεύομαι ἑτοιμάσαι τόπον ὑμῖν·

(The punctuation for a question mark is &quot;;&quot;, which does not appear)