WASHINGTON, July 16 (Reuters) - Senate Banking Committee Chairman Christopher Dodd said on Wednesday that he thought the U.S. Senate would be able to vote on a rescue package for mortgage finance giants Fannie Mae (FNM.N: Quote, Profile, Research) and Freddie Mac (FRE.N: Quote, Profile, Research) next week.

Dodd, a Connecticut Democrat, has been working with the administration and fellow lawmakers to help craft the legislation that the administration hopes will help restore public confidence in those shareholder-owned but government-sponsored enterprises.

Dodd said lawmakers and staff were working through the issues and the Senate and U.S. House of Representatives were working out differences on the underlying housing legislation.

When asked by reporters if the Senate would be able to vote on the bill next week, Dodd said "I think so." (Reporting by Donna Smith; Editing by James Dalgleish)