I am planning to get a Fender 65 twin reverb reissue, and I am wondering if it's possible to connect it to an audio interface, a Focusrite 2i4, for example?
With a 2i4 you have the option of using two inputs so I would suggest tracking either two microphones (for instance an SM57 on the cone, and something sweet like an Aston Spirit or another LDC of your choice on room mic, a couple of foot back to try and get the developed sound of the room.)
This should give you the option of developing a nice balanced tone on each and every take.
Failing this, and since the amp in question is a tube amp I would advise against, muting the speakers and going with some form of DI as mentioned above as this can be detrimental to the speaker circuit. You'd be better suited with an attenuator so the amp actually feels like it has some form of load (resistance) on it
The best way to record an amp like that would be to put a mic in front of it and connect the mic to the interface.
The second best way would be to use a speaker simulator/DI that can be inserted in between the speaker out of the amp and the speakers, and then the XLR out from the speaker sim/DI would be connected to the interface.
It does not seem to have a line output or any other kind of output so those are probably your only options.