While the answers that point out that a system needs to be LTI to have a transfer function is correct, there isn't a lack of trying.
Tymerski, Richard. "Application of the time-varying transfer function for exact small-signal analysis." IEEE Transactions on Power Electronics 9.2 (1994): 196-205.
Kamen, Edward W., Pramod P. Khargonekar, and K. R. Poolla. "A transfer-function approach to linear time-varying discrete-time systems." SIAM journal on control and optimization 23.4 (1985): 550-565.
these are only a few Google hits. There is more.