The Reds have been without a permanent manager since sacking Matt Beard in February, with Amber Whiteley taking charge on an interim basis for the remainder of 2024-25.
Taylor was sacked by City in March just five days before the Women's League Cup final.
The Welshman began working with City's academy in 2011 and was appointed head coach in 2020.
He won the FA Cup during his first season and led the club to League Cup glory in 2022, while his side missed out on the Women's Super League (WSL) title on goal difference in 2023-24.
Liverpool finished seventh last season, 35 points adrift of champions Chelsea.
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