New York City Mayor Bill de Blasio’s administration is unlikely to seek a cap on growth in for-hire car services such as Uber, a proposal that failed to gain traction after Mr. de Blasio floated it last summer, according to people familiar with the matter.

City Hall is expected this month to release the results of a study exploring whether growth in Uber and other for-hire vehicle trips is contributing to worsening congestion in Manhattan’s central business district.

As...