The 20-year-old wing is under contract at the Llanelli-based Scarlets, where he has another year of his existing deal remaining, but North's agent Christian Abt revealed earlier this month that the Saints and Scarlets were in talks about his client.
And the Chronicle and Echo newspaper in Northampton reported on Thursday that Saints chairman Leon Barwell had confirmed an offer to North from the Aviva Premiership club.
"It's a big decision for George and we don't want to put undue pressure on him," Barwell 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 are giving him some time and space to do that."
North, who was born in England but moved to north Wales at the age of two, is among European rugby's hottest properties.
He made his Test debut as an 18-year-old against South Africa in 2010, scoring two tries, and was an integral part of Wales' 2011 World Cup campaign, helping them reach the semi-finals. North's career also includes two RBS 6 Nations title successes with Wales and a Grand Slam.
But the Welsh game is currently engaged in a battle to keep its big names playing in the Principality. Mike Phillips, James Hook and Luke Charteris are among those who ply their trade in the French club game, with centre Jamie Roberts and flanker Dan Lydiate set to join them next season by heading to Paris-based Racing Metro.
A cross-border switch for North, though, would arguably be the most high-profile departure of them all.