In distributed storage systems, codes with lower repair locality are much more desirable due to their superiority in reducing the disk I/O complexity of each repair process. Motivated partially by both codes with information (r,δ₁)_c locality and codes with cooperative (r,l) locality, we propose the concept of codes with information (r,l,δ) locality in this paper. For a linear code C with information (r,l,δ) locality, values at arbitrary l information coordinates of an information set I can be recovered by connecting any of δ existing pairwise disjoint local repair sets with size no more than r, where a local repair set of l coordinates is defined as the set of some other coordinates by which one can recover the values at these l coordinates. We derive a lower bound on the codeword length n for [n,k,d] linear codes with information (r,l,δ) locality. Furthermore, we indicate its tightness for some special cases. Particularly, some existing results can be deduced from our bound by restriction on parameters.