Turkmenistan's state media issued the reports as international competition for access to that former Soviet republic's oil and natural-gas resources intensifies.
Berdymukhamedov met with Chevron executives on May 3 in Ashgabat.
He is due to meet Russian President Vladimir Putin and Kazakhstan's President Nursultan Nazarbaev on May 11.
Putin said in April that Moscow hopes to work on energy projects with Turkmenistan.
(compiled from news agency reports)