The Nord Stream project is part of a network of pipelines planned to diversify Russian natural gas export routes to European consumers. The first leg of Nord Stream went into service last year.
Alexei Miller, the top executive at Gazprom, in June said European demand for natural gas would justify the construction of the new legs, which would increase its capacity to more than 3.8 trillion cubic meters per year.
Project company Nord Stream AG asked for permission from the Estonian government to conduct a study in its economic zone through the end of 2014 for consideration for possible additional lines, the Interfax news agency reports.
The country took part in the consultation process for the first two lines but refused a study request in 2007. Estonian Prime Minister Andrus Ansip said it was too early to draw any conclusions about Nord Stream AG's request.
"I don't want to get ahead of events and can't say right now what decision the government will make this time," he was quoted as saying.