With Warren Gatland in charge of next summer's tour to Australia and North's form of late, the Scarlets man is seemingly a shoo-in to make the trip.
And Woodward, who took up the role of director of sport for the British Olympic Association in 2006 and helped manage Team GB's efforts at Beijing 2008 and London 2012, would also like to see him at Rio 2016, when rugby sevens makes its bow on the Olympic stage.
"It's like you would pick a Lions team, you'd pick your dream sevens team and it's probably more difficult to pick a sevens team," said Woodward, who took charge of the 2005 Lions tour to New Zealand.
"George North would certainly make my Lions team at the moment. Would he make my sevens team, yes.
"You're trying to pick this team, but he's got to play [sevens], you can't just put him in to that level. The fitness is a little bit different.
"So certainly a year out, you'd like to think post-World Cup you're only 12 months away [from the Olympics] so a few players, a couple from each country, coming in.
"They're big names, but you're not picking them for their names. Can they play sevens? Can they go and win a gold medal?"