"We got in contact with the Swedish authorities a while ago. At the moment it is a question of preparing our next step," said Shaher Abbas for IBB.
The Islamic Bank of Britain was formed in 2002 with the aim of meeting the financial needs of the British Muslim population and is backed by investors in the Middle East.
IBB now offers internet banking and savings products and has 60,000 customers at its eight branches across the UK.
The company is now planning a European expansion with branches in Germany and Sweden, according to Sveriges Radio.
IBB's business is based on the principles of Islamic finance which stipulate that savings and loan products are offered without the use of interest.
"We make every effort to ensure that we do not compromise the principles of the Islamic faith by mixing our funds with interest bearing funds. We fund all our operations on a Sharia'a compliant basis," the company explains on its website.
Despite its profile, the Islamic Bank of Britain welcomes both Muslim and non-Muslim customers.
"We have Christian customers, Sikhs and many non-religious customers also," Abbas told Sveriges Radio.
The bank is regulated by the Financial Supervisory Authority (FSA) in the UK and is also subject to and approved by a Sharia'a Supervisory Committee - made up of three learned members of the British Muslim community.
Although the IBB would be Sweden's first bank based on the Islamic principles of Sharia'a, it would not be the first to seek to avoid the use of interest bearing funds.
JAK members bank has been operating interest-free savings and loans under a banking licence since 1997. JAK is formally a cooperative bank with 35,000 members and a growth of around 5 percent per annum.
JAK is not a religious bank but has a certain missionary zeal and declares on its website:
"We at JAK work for a society with financial rules which do not create huge divisions between people and regions. For a just society without interest!"
JAK, a bank borne of 1970s idealism and thriving in a decidedly different age some three decades later, could soon be joined by a bank with a code of principles as old as the religion of Islam itself, and great ambition to boot.
"I think we can be much bigger, God willing," said Saher Abbas to Sveriges Radio.