Western Union, which allows consumers to transfer money to friends and family in other countries, had a global turnover of £3.25bn last year.
Tesco is waiting on approval from the Financial Services Authority before it can roll out a similar money transfer service to its stores. It is understood to be aiming the service not only at its customers, but also at its 286,000 UK members of staff.
The company currently has six bank branches and is planning to open 30 by the end of the financial year.
"Tesco is building a different kind of bank one that listens to customers, offers simple and transparent products and rewards loyalty," said Tesco Bank chairman Andrew Higginson.