This work focuses on the relation between the electron density and the magnetic field strength in the solar wind, and aims to reveal its compressive nature and to determine the level of compressibility. For this purpose, we choose a period of quiet solar wind data obtained at 1 AU by the ClusterC1 satellite. The electron density is derived with a sampling time as high as 0.2 s from the spacecraft-potential measurements made by the Electric Field and Waves instrument. We use the wavelet cross-coherence method to analyze the correlation between the electron density and the magnetic field strength on various scales. We find a dominant anti-correlation between them at different timescales ranging from 1000 s down to 10 s, a result which has never been reported before. This may indicate the existence of pressure-balanced structures (PBSs) with different sizes in the solar wind. The small (mini) PBSs appear to be embedded in the large PBSs, without affecting the pressure balance between the large structures. Thus, a nesting of these possible multi-scale PBSs is found. Moreover, we find for the first time that the relative fluctuation spectra of both the electron number density and the magnetic field strength look almost the same in the range from 0.01 Hz to 2.5 Hz, implying a similar cascading for these two types of fluctuations. Probable formation mechanisms for the multi-scale possible PBSs are discussed. The results of our work are believed to be helpful for understanding the compressive nature of solar wind turbulence as well as the connections between the solar wind streams and their coronal sources