That would fit a context such as KdrV A224/B271, where Kant equates [den Begriff eines Triangels] konstruieren (to construct/construe the concept of a triangle) with to give [the concept] an object, i.e. to give it what he elsewhere calls a reference [Beziehung] to objects, and hence a significance [Bedeutung] (A1456/B185), or, taking Bedeutung more broadly: to give it an imagined significance [eingebildete Bedeutung] (A84/B117), as opposed to a mere logical significance (A147/B186). To construe, that is, interpret, is to give significance.
Unfortunately, this appears not to be an accepted sense of the German verb (and moreover, according to the OED, is only a late and derivative sense of the English one). Moreover, we have to take into account another use of konstruieren in the exact same passage (from the proof of the First Postulate). Kant also talks there about the synthesis wodurch wir in der Einbildungskraft einen Triangle konstruieren (A224/B271). Whatever that means, it doesnt mean by which we construe (= interpret) a triangle in the imagination.
Many would take it, instead, to mean something like: by which we construct (= build up) a triangle out of imaginary pieces, using an imaginary compass and an imaginary ruler, on a piece of imaginary paper. But that in itself makes little sense. Moreover, to the extent that it does make sense, it leads straight back to Descartess argument that we cant do any such imaginary drawing in the case of a chiliagon (a point of which Kant is well aware: see A140/B17980). Finally, such an understanding of konstruieren wouldnt work at all in the first example, where Kant talks of constructing the concept of a triangle. A concept presumably cant be drawn on any paper, no matter how imaginary.
So my new thought is this: that both of these ways of talking are short for: einen Begriff mit einem Gegenstand konstruieren, to construe a concept with an object (on the model of: to construe a verb with an object).
If we can construe a concept with an object (via a schema), then we know that it is at least the concept of an ens imaginarium (not, like the concept diangle, that of a nihil negativum [A291/B348]; and not, of course, of an ens rationis or nihil privativum, either). What hes saying in the proof of the First Postulate (i.e., the proof that what agrees with the formal conditions of experience (according to intuitions and concepts) is possible [A218/B265]) is that to promote a concept from the concept of an ens imaginarium (which, although not impossible, is still a kind of nothing) to the concept of a possible being, we need to connect the procedure of the imagination in the schema of that concept to the synthesis of the imagination in perception.
So the object of the concept triangle would remain always only a product of the imagination if it were not that
The very same [eben dieselbe] imaging synthesis by which we construe a triangle [with its concept] in the imagination is wholly the same as [mit einerlei] that which we exercise in the apprehension of an appearance, in order to make from it an empirical concept. (again, A224/B271)
The concept triangle passes this test, but the concepts of pure time and pure space as such, die zwar Etwas sind, als Formen anzuschauen, aber selbst keine Gegenstände sind, die angeschaut werden [A291/B347], do not. The synthesis by which the pure imagination produces time and space as pure images of the categories is not the same as any synthesis of the empirical imagination in perception (but is rather a condition of possibility of all such empirical synthesis). Hence the concepts of time and space are concepts of entia imaginaria.1
However, Im not sure yet if this will work in other places or whether Kant anywhere actually uses the locution to construe a concept with an object.
1 The ursprünglich pure intuitions of time and space, I take it, do not have objects: intuitions without concepts are blind.