Shell is one of the companies with plans to explore for oil in arctic waters. Greenpeace vessels were reportedly trailing Shell's drill ships near the Alaskan coast recently.
Greenpeace activist Sara Ayech was quoted by the BBC as saying her group was planning to shut down Shell's refueling stations in London and Edinburgh to protest arctic drilling plans.
"The arctic must be saved and made a global sanctuary where oil drilling is banned," she said.
A spokesman for the oil company said an offer to have "productive dialogue" was extended to Greenpeace.
Activists last week were arrested after protesting in front of Shell's headquarters in The Hague, Netherlands.
Last week, U.S. Sen. Lisa Murkowski, R-Alaska, called on federal authorities in the United States to find out what sort of legal mechanisms were in place to ensure Greenpeace protests planned near Shell's operations in Alaska were safe.
"Allowing intrusions by any group to disrupt or threaten federally permitted operations is a direct threat to the careful planning and safe operations necessary for these activities and puts in jeopardy those workers and our environment," Murkowski stated in a letter to regulators.