The resignation on Tuesday, which comes amid a heated debate in the Gulf state over a proposal to amend the election law, has not yet been accepted.
It becomes official only after Sheikh Sabah al-Ahmad al-Sabah, the amir, signs it.
The resignation has not been carried by the state-run media although it was reported by some local newspapers, quoting unnamed sources.
Rasheed, 38, a liberal academic who was appointed to the post in March last year, has objected to the principle of amending the constitution which was promulgated in 1962.
One official told Reuters: "The minister resigned because he rejects the government's support for amending the constitution."
The amendment, discussed by the cabinet in an extraordinary meeting on Monday night, aims to increase the number of MPs in the fully-elected parliament from 50 to 60, the source said.
The oil-rich emirate has been gripped by a debate over measures to cut the number of constituencies from 25 to five amid accusations that the small electorates created by the current system paved the way for vote-buying.
The cabinet has so far failed to reach a decision on the issue despite holding several extraordinary meetings.
Supporters and opponents of the reform bill have been holding daily public rallies to drum up popular support.
The bill is expected to be submitted to parliament on May 15 if it wins cabinet approval.