Northampton have offered a deal to the 20-year-old, who has one year remaining on his Scarlets deal.
Saints would be forced to pay a fee to tie up a move for North, but that is something they are prepared to do.
The winger, who has scored 12 tries in 31 Test appearances for Wales, fits the bill as director of rugby Jim Mallinder looks to add ammunition to his backline.
Mallinder is understood to have met with the player in a bid to iron out a deal and the ball is now firmly in North’s court, according to Barwell.
“There’s been strong speculation linking us with George North but at the end of the day it’s up to George to weigh up his options,” said the chairman.
“We would really only want to progress a deal with him on the basis that he wants to come to Northampton.
“He’s taking the time at the moment to weigh up his options.”
Scarlets boss Simon Easterby said last week it would be a ‘disaster’ for Welsh rugby to lose prized asset North to the English game.
And Barwell is keen to ensure the player will be fully committed to the Saints cause before pen is put to paper.
“It’s a big decision for George and we don’t want to put undue pressure on him,” he said.
“He’s got to make sure that when he makes the decision it’s the right one for him as an individual on the basis he really wants to come to Northampton.
“We’re giving him some time and space to do that.
“Obviously any player that comes to Northampton we want them to come here on the basis that they’re going to be committed to the club and they see it as a positive step forward for them.
“That’s where the ball lies.”