Valence and conduction bands in nodal loop semimetals (NLSMs) touch along closed loops in momentum space. If such loops can proliferate and link intricately, NLSMs become exotic topological phases, which require nonlocal hopping and are therefore unrealistic in conventional quantum materials or cold atom systems alike. In this Letter, we show how this hurdle can be surmounted through an experimentally feasible periodic driving scheme. In particular, by tuning the period of a two-step periodic driving or certain experimentally accessible parameters, we can generate arbitrarily many nodal loops that are linked with various levels of complexity. Furthermore, we propose to use both a Berry-phase related winding number and the Alexander polynomial topological invariant to characterize the fascinating linkages among the nodal loops. This Letter thus presents a class of exotic Floquet topological phases that has hitherto not been proposed in any realistic setup. Possible experimental confirmation of such exotic topological phases is also discussed.