We study the mean first time that two monomers, located on the same polymer, encounter in a confined microdomain. Approximating the confined geometry by a harmonic potential well, we obtain an asymptotic expression for the mean first encounter time (MFETC) as a function of the radius ε around one monomer. By studying the end-to-end distance of the polymer in a ball using the Edwards’ formalism, we derive an other estimation of the MFETC. We validate the asymptotic formulas using Brownian simulations and derive their range of validity in terms of the polymer length. We apply the present models to compute the mean time for a gene located far away from a promoter site to be activated during looping in confined genomic territories. [ABSTRACT FROM AUTHOR]