LONDON (AP) _ Nancy Reagan's ''inflexible goal'' for the remaining 16 months of her stay in the White House is to see President Reagan win the 1988 Nobel Peace Prize, according to the Sunday Express.

The weekly newspaper, in a report attributed to what it called close friends of the Reagans, said Mrs. Reagan's ''rock-hard determination'' is pushing the president to reach an arms treaty with the Soviet Union and to bring peace to the Persian Gulf and Central America.

It did not identify those friends but reported they said wealthy industrialist Armand Hammer has been enlisted to talk with Nobel Prize officials at a meeting in New York next month.

It also reported other unidentified sources said Hammer, chairman of Occidental Petroleum Co., has already conferred with Nobel officials in Oslo, Norway. The Sunday Express said John King, a spokesman for Hammer, denied that report.

The newspaper quoted what it called a senior presidential adviser as saying: ''In the end, everyone knows the President listens to Nancy.

''Now Nancy has made up her mind that Ronald Reagan is not going to leave after eight years in the White House with the stigma of the Iran-Contra scandal as his legacy.

''She has convinced him that he can bring an end to the Gulf War by forcing Iran to stop shooting, get the Central American situation settled and cap it with two nuclear missile pacts in 1987 on medium and shorter range missiles and reductions of intercontinental missiles in 1988.

''That is the monument she wants for him to be acknowledged in the form of a Nobel award.''