Let $M$ be a smooth simply connected manifold and let $N$ be $M$ minus a point. Is it possible to construct an explicit Sullivan model for $N$ (i.e. a commutative differential graded algebra (cdga) which is connected to the algebra of $\mathbf{Q}$-polynomial forms on $N$ by a chain of cdga quasi-isomorphisms) starting from the minimal Sullivan model for $M$?

[upd: in principle the above question is a very particular case of the one discussed in the paper Algebraic models of Poincar'e embeddings by P. Lambrechts and D. Stanley, AGT 5, 2005. That paper discusses general polyhedra that satisfy some connectivity/codimension assumptions, which are certainly true when the polyhedron is a point. But the general construction involves some non-canonical choices and I was wondering if there is a cleaner and more ``canonical'' construction when the polyhedron to be thrown away is simply a point.]