The Wales and British and Irish Lions full-back's contract with the French club expires at the end of 2016-17.
Cardiff Blues would be favourites to sign Halfpenny, with Scarlets also interested.
"It's a head versus heart decision for Leigh," said Phillips.
"We will hope he comes back, but he's his own man and I would respect his decision, whatever it is."
Halfpenny joined Toulon from Blues in 2014 and if he returns to Wales, it would be on a National Dual Contract in which the WRU would pay 60% of his salary and his region the rest.
He has scored 606 points at international level, 557 of them for Wales and the rest as the Lions' goalkicker as they beat Australia 2-1 in 2013.
Phillips added: "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."
Phillips also defended the decision to allow Rob Howley to join Warren Gatland as part of the Lions set-up next summer.
"I think Warren and Rob will both benefit as coaches from the Lions experience," added Phillips.
"I don't think the South Sea Island tours will be hugely beneficial to them.
"We genuinely have to give some coaches exposure so I am comfortable with that decision."
The Welsh Rugby Union has made "the best offer it can" to bring Leigh Halfpenny back from Toulon, says governing body chief executive Martyn Phillips.