Tracking valence electron motion in molecules is the key to understand and control chemical transformations. Contemporary techniques in attosecond science have the capability to generate and track the consequences of this motion in real time, but not in real space. Consequently, the local time-evolution of the electron density can so far only be inferred by reconstruction from the (often elusive) features appearing in electron, ion, absorption or emission spectra, mainly in small molecules. Scanning tunnelling microscopy (STM), on the other hand, can locally probe the valence electron density in molecules, but cannot provide by itself dynamical information at this ultrafast time scale. Here, we demonstrate that, by combining STM and attosecond technologies, the dynamics of a coherent superposition of valence electronic states generated by < 6 femtosecond long carrier-envelope-phase (CEP) stable laser pulses can be directly and simultaneously visualized with picometer spatial resolution and 300 attosecond temporal resolution, thus going well beyond the previously established space-time limits and bypassing any kind of reconstruction. In particular, we show that near fields of near-infrared pulses confined to the apex of a nanotip of an STM enable concurrent real-space and real-time imaging of the valence electron dynamics generated in the perylenetetracarboxylic dianhydride (PTCDA) molecule, as well as exerting full control of the electron density in the highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbitals. We envision that this approach could thus open the way to the unambiguous observation and manipulation of electron dynamics in complex molecular systems, in monolayer thick 2D materials and in superconductors.