Fonua-Blake remains one of the hottest properties on the NRL market for 2025, and was due to meet with several Sydney clubs in the past few days.
After requesting a release from the Warriors earlier this month, the 28-year-old will stay put for next season but is eyeing a move to Sydney for 2025.
The Dragons are among the leading contenders for the the front-rower's signature, with Wests Tigers and Canterbury also known to be in the market.
Fonua-Blake has links back to the Dragons as a junior, making a mark on the likes of a teenage Lawrie when he assisted younger players in training sessions.
"It'd be huge. I would obviously love to play with him," Lawrie said.
"I remember when he was at Manly. He's got the best footwork as a front-rower.
"This year at the Warriors, he is a guaranteed top-three prop in the comp, if not No.1. You can argue for him to be No.1."
Lawrie was the Dragons' stand-out forward last year, but the club could desperately do with more starch up front.
"To play alongside him, it will make everyone's job a lot easier," Lawrie said.
"Because of the presence that he has and the quality of player he is.
"He's a world-class player and he demands respect.
"The stats and numbers speak for itself with the style of game he plays. He takes three to four plays to bring him down."
Joey Manu was also floated as a potential target, but Flanagan has since conceded he is unlikely to leave the Sydney Roosters.
"We are two or three players quality plays away from being a really good footy side," Flanagan said.
"I saw that at the Sharks. All of a sudden we got James Maloney who wasn't wanted by the Roosters, Michael Ennis who wasn't wanted by the Bulldogs.
"Luke Lewis who wasn't wanted by Penrith, and then Chris Heighington, players like that change the whole thing.
"We don't win the comp in 2016 if we don't get them. We went from zero and last in 2014 to winning the comp.
"People don't realise how close it is here. But we need to have a bit of luck about getting quality players.
"Those players we've spoken about all fit into that category. They're quality. We can build our next two or three years in and around those quality players."
- Australian Associated Press