London City Lionesses are an ambitious club under owner Michele Kang and had a steady debut campaign in the WSL, finishing sixth after eight wins from 22 matches.
Sources at the club say an agreement with Earps has not yet been made, but they remain optimistic about their summer business.
Eder Maestre’s side have been linked with several players including Barcelona defender Mapi Leon and England winger Beth Mead, who announced her departure from Arsenal this week amid additional interest from Manchester City.
Earps is one of a number of big-name players potentially available on a free deal this summer, with Arsenal’s Mead and Katie McCabe leaving, Barcelona’s Alexia Putellas yet to sign a new contract, Sam Kerr departing Chelsea and Manchester City top scorer Khadija Shaw rejecting contract renewal proposals.
During her time in England, Earps became one of the country’s most recognised and influential players, though her book – released in November – caused controversy and dominated headlines in the media for several weeks.