Malaysia ditched plans to replace an ageing causeway linking the countries, saying Singapore's demands for airspace access and sand for reclamation projects in return for its agreement was unacceptable.
The two neighbours have squabbled for years over a variety of issues, but while many other feuds have been settled, the bridge remained a thorny topic.
"Why can't we have a bridge and remove the old causeway?" Sultan Ibrahim Ibni Almarhum Sultan Iskandar, the ruler of southern Johor state which borders Singapore, told the Star newspaper.
"It must be a one-for-one kind of deal. No one should be on the losing end," he said.
The sultan said he was against building a third link to the island-state. Apart from the causeway, Malaysia and Singapore already have a second link that was completed a decade ago.
Sultan Ibrahim, who became the state's royal ruler after the death of his father in January, offered to be the mediator in resolving several outstanding issues between Malaysia and Singapore.
They include the price of water supplied to Singapore, and extending Singapore's mass rapid transit railway into Johor, according to the report.
"I think some of the issues between Johor and Singapore can be resolved over a cup of tea," he said according to the English-language daily
"The congestion is bad on both sides of the causeway. We need to improve the public transportation system."
Relations have often been stormy since Singapore left the Malaysian federation in 1965 over ethnic issues but they have undergone a marked improvement in recent years, especially in economic cooperation.