The outbreak of Coronavirus disease 2019 (COVID-19) has resulted in a serious pandemic situation which the world is going through since the beginning of the year 2020. Given this, the infected countries are constantly increasing their lockdown period and therefore, experiencing an adverse impact on their socio-economic structure. With these motivations, this paper is an attempt to estimate the time that a country would take more to recover from COVID-19 situation. In this work, for curve fitting, the polynomial model has been used deliberately for easier interpretation of the technique. The methodology captures the characteristic trends of the already flattened curves from recovered countries and utilizes them to estimate the curve flattening time for the infected countries. The approach requires only the minimum set of data, i.e., the number of infected persons per day for a given country.