  We propose a possible modification to the tensionless string model with
contact interactions. The proposed model aims to reproduce an expectation value
of the non-Abelian Wilson loop in the Yang-Mills theory when integrating out
string degrees of freedom with a fixed worldsheet boundary. Lie algebra-valued
fields whose dynamics are determined by the topological BF action are
introduced on the string worldsheet to reproduce path-ordering along the
worldsheet boundary. Without bulk contributions, we show that the model
describes the non-Abelian Wilson loop discarding effects of self-interactions.
Finally, a reproduction of the Wilson loop with three-point interaction is
tested in the case of $SU(2)$
