We present Karl G. Jansky Very Large Array (VLA) observations of the CO ($J=2\to 1$) line emission towards the $z=6.419$ quasar SDSS J$114816.64+525150.3$ (J$1148+5251$). The molecular gas is found to be marginally resolved with a major axis of $0.9"$ (consistent with previous size measurements of the CO ($J=7\to 6$) emission). We observe tentative evidence for extended line emission towards the south west on a scale of ~$1.4"$, but this is only detected at $3.3\sigma$ significance and should be confirmed. The position of the molecular emission region is in excellent agreement with previous detections of low frequency radio continuum emission as well as [C ii] line and thermal dust continuum emission. These CO ($J=2\to 1$) observations provide an anchor for the low excitation part of the molecular line SED. We find no evidence for extended low excitation component, neither in the spectral line energy distribution nor the image. We fit a single kinetic gas temperature model of 50 K. We revisit the gas and dynamical masses in light of this new detection of a low order transition of CO, and confirm previous findings that there is no extended reservoir of cold molecular gas in J$1148+5251$, and that the source departs substantially from the low $z$ relationship between black hole mass and bulge mass. Hence, the characteristics of J$1148+5251$ at $z=6.419$ are very similar to $z$~$2$ quasars, in the lack of a diffuse cold gas reservoir and kpc-size compactness of the star forming region.