Novye Izvestia said the 39-year-old son of the Turkmen leader had reached an agreement on opening Emirates flights to the Central Asian republic's capital, Ashgabad, Turkmenistan's regular participation in Dubai trade expositions and establishing a consulate general in the United Arab Emirates.
The paper said Saparmurat Niyazov, who prefers to go by the moniker "Turkmenbashi", father of all Turkmen, had tackled such issues in the past.
In 2003, Niyazov, who was declared president-for-life by the Turkmen parliament in 1999 and has built a personality cult around himself since the independence from the Soviet Union in 1991, said he would step down when he turned 70 in 2010 and proposed holding presidential elections in 2009.
Novye Izvestia said parliament was yet to make a decision on the issue.
Murad, who the paper cites reports as running an oil and natural gas business in Vienna, was given broad powers in the Dubai talks, which prompted some experts to say that the Turkmen president intended to follow in the footsteps of the late Azerbaijani leader Heidar Aliyev and make his son the successor.
But a political analyst in neighboring Kazakhstan, Konstantin Syroyezhkin, cast doubt on this possibility. "Niyazov is a political loner and has no developed system of family connections, therefore, he can have no heir," he said.
Dmitry Aleksandrov, an expert with the Russian Strategic Research Institute, said under certain conditions Niyazov could formally hand over the reins to a puppet and keep real power in the country for himself.