We experimentally investigated the effect of a neighboring liquid droplet on fluid convection inside a liquid droplet of aqueous solution present inside a microchannel using the microscale particle image velocimetry technique. There is no physical contact between the two droplets, and the solute concentrations of the two droplets are set at different values. Vapor concentration near the interface of the two droplets is different due to the difference in solute concentration. Water vapor evaporates from the low-concentration droplet having higher vapor pressure and condenses on the high-concentration droplet having lower vapor pressure. Evaporation and condensation induce Rayleigh convection inside the two droplets. Flow pattern shows circulating loops inside both liquid droplets. The circulations at the interacting adjacent interface of the two droplets are opposite to each other. The strength of flow inside the liquid droplets decreases with time due to decrease in the difference of solute concentration between the two droplets. The flow strength inside the two interacting droplets is also a function of separation distance between the droplets. The flow strength inside the droplets decreases with increase in separation distance.