Monte Carlo simulations are conducted to investigate a model composed of a fluctuating sphere labeled on one chain end of an isolated flexible chain polymer in good solvents. The labeled sphere is to model the instantaneous size of a bound flexible chain segment or a vibrating chromophore on a polymer chain. We assume the vibration of the sphere is governed by a harmoniclike potential, and the sphere size stays positive. We first address the issue regarding the confinement effect induced by a flexible chain. To rationalize the simulation results, we carry out a detailed analysis for a simple case containing a dimer grafted onto a fluctuating sphere. Using the sphere with a large size fluctuation, we find that the fluctuating sphere can be confined within the coiled polymer chain, and even trapped inside the grooves between neighboring monomers. The results imply the confinement effects may influence the properties of chromophores labeled on polymers or drugs bound to biopolymers. Moreover, in a separate study, we show the fluctuating sphere model can be used to fit a bound flexible chain segment, and provides a means to parameterize a polymer chain to a dumbbell, with possible applications in the dynamics of dilute polymer solutions.