The 28-year-old is out of contract with the French club at the end of the 2016-17 season and has been tipped with a return to Cardiff Blues.
WRU chief executive Martyn Phillips claims that the ball is now in Halfpenny's court, with his three-year spell in France likely to be nearing its conclusion.
"It's a head versus heart decision for Leigh," Phillips is quoted as saying by BBC Sport. "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."
Should Halfpenny return to his homeland, it will be part of a National Dual contract in which more than half of his salary is paid by the WRU and the rest by his regional side.