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A new subclass of bi-close-to-convex functions associated with the generalized hypergeometric functions defined in ∆<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>=</mo><mo>{</mo><mi>z</mi><mo>∈</mo><mi mathvariant="double-struck">C</mi><mo>:</mo><mo>|</mo><mi>z</mi><mo>|</mo><mo><</mo><mn>1</mn><mo>}</mo></mrow></semantics></math></inline-formula> is introduced. The estimates for the general Taylor–Maclaurin coefficients of the functions in the introduced subclass are obtained by making use of Faber polynomial expansions. In particular, several previous results are generalized.