The 33-year-old skippered the Swans to Premier League promotion in 2011, but was told he will not feature in Laudrup's first-choice XI and could leave, with the Robins interested
The Championship side are reportedly set to swoop for the experienced centre-back should he decide to leave in search of first-team football.
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"I spoke to him a couple of weeks ago and said it will be difficult for him to play in the starting XI. He is now making up his mind."
The 33-year-old has made over 200 appearances since signing for the club in 2004, captaining the Swans when they won promotion to the Premier League in the 2011 Championship play-off final against Reading.
New signing Chico has started both the Swans’ opening matches alongside Ashley Williams after signing from Genoa, replacing Steven Caulker who returned to Tottenham after his loan spell at the club ended at the end of last season.
The former Denmark international gave Monk his blessing should he depart, adding: "I think he will make the right decision for himself whatever that is – either staying here or going somewhere else for the next couple of seasons.
"I always say it is easy to smile and shake hands for the picture when people arrive. But it’s nice to shake hands when they leave and that doesn’t happen often in this world of football."