The recognition and pairing of specific DNA loci, though crucial for a plenty of important cellular processes, are produced by still mysterious physical mechanisms. We propose the first quantitative model from Statistical Mechanics, able to clarify the interaction allowing such "DNA cross-talk" events. Soluble molecules, which bind some DNA recognition sequences, produce an effective attraction between distant DNA loci; if their affinity, their concentration, and the relative DNA binding sites number exceed given thresholds, DNA colocalization occurs as a result of a thermodynamic phase transition. In this paper, after a concise report on some of the most recent experimental results, we introduce our model and carry out a detailed "in silico" analysis of it, by means of Monte Carlo simulations. Our studies, while rationalize several experimental observations, result in very interesting and testable predictions. Copyright (C) 2009 A. Scialdone and M. Nicodemi.