Singapore Prime Minister Lee Hsien Loong and Malaysian Deputy Prime Minister Najib Razak discussed this matter on the sidelines of the Asia-Pacific Economic Cooperation (Apec) summit in Peru last week, reported Malaysian daily Berita Harian.
This was confirmed by a Singapore government spokesman.
Describing the issues as a 'thorn in the flesh' of their countries' bilateral relations, Berita Harian reported Datuk Seri Najib as saying that the two leaders discussed the measures which could be implemented to resolve these issues, in the best interest of both countries.
According to the report, the outstanding matters include: the continued supply of water from Malaysia to Singapore after the current pact expires in 2061; the use of Malaysian airspace by Singaporean military aircraft and allowing West Malaysians working in Singapore to withdraw their Central Provident Fund savings.
There is also the issue of building a new bridge to replace the Causeway, as well as an unresolved agreement on Malayan Railway-owned land in Tanjong Pagar in Singapore.
The issue of railway land involves one of the Points of Agreement that the two countries had signed in 1990.
As part of that agreement, Malaysia would move the Keretapi Tanah Melayu (KTM) station from Tanjong Pagar to Kranji, with trains running in an underground tunnel from Johor to Kranji train station.
It also agreed to shift its Customs, Immigration and Quarantine (CIQ) facilities to Kranji when the tunnel is completed.
But Malaysia later changed its mind. It kept its CIQ facilities at Tanjong Pagar, even after Singapore had moved its own CIQ to the Woodlands Train Checkpoint.
Mr Najib said that Malaysian Foreign Minister Rais Yatim will be meeting his Singapore counterpart George Yeo to discuss the outstanding issues.
These issues, which have tested bilateral relations, were to have been discussed as a package, as proposed by then-Malaysian prime minister Mahathir Mohamad in 1998.
But negotiations were beset with complications when senior officials met. Malaysia later decided it no longer wanted to discuss the issues as a package.