Interest in the 24-year-old is mounting after his starring role in the British and Irish Lions' success in Australia, where he was later named player of the series.
Reports have suggested that clubs in France are monitoring the situation, but Blues chief executive Richard Holland said that the club will strive to secure his future at Arms Park.
"Whether or not Leigh will stay I don't know, but he's a Welsh lad and we're hoping he will commit to the Blues," he told The Independent. "We have already had discussions and we will be working hard with Leigh to lock him into the Blues for the foreseeable future.
"We are extremely proud of the achievements of all our Lions. Leigh must be the only candidate for the IRB's World Player of the Year after destroying Australia.
"Now we are going to do everything in our power to secure his services. We're trying to put together, within our means, a package which will enable Leigh to stay at the Arms Park and in Welsh rugby."
Halfpenny made his debut for the Blues against Ulster in 2008.