He currently plays in France with Toulon
The Welsh Rugby Union (WRU) have made an offer to bring Leigh Halfpenny home when his current contract with Toulon expires.
His contract is due to end at the conclusion of this season and the WRU have made "the best offer it can" in an attempt to bring one of their international stars home.
Speaking to the BBC, chief executive Martyn Philips said: "It's a head versus heart decision for Leigh. We will hope he comes back, but he's his own man and I would respect his decision, whatever it is.
"We have made him the best offer we possibly can. The clock is ticking now. It's at a point where Toulon would want some certainty some time in the next couple of weeks.
"Any way you look at it, you would want to have Leigh playing in Welsh rugby. On the pitch he's a winner and off the pitch he's an ambassador for Welsh rugby.
"When you ask little kids, who is their favourite player many of them would say Leigh Halfpenny," he added.
Halfpenny joined the French club in 2014. He has played 66 times for Wales scoring 557 points. He also played a key role in the 2013 Lions series win over Australia.