Baptista has played for the likes of Sevilla, Arsenal, Real Madrid and Roma during his career, but the 35-year-old is currently a free agent after being released by Orlando City.
According to The Sun, Bolton are ready to try to take advantage of his availability by launching an ambitious move for the veteran ahead of the start of the new campaign.
During his previous time in England during the 2006-07 season, Baptista netted three goals in 24 Premier League appearances for the Gunners.
The Trotters are preparing for their return to the Championship after gaining automatic promotion from League One after just a year back in the third tier.
Manager Phil Parkinson has brought in seven new signings ahead of their opening fixture at home to Leeds United on Sunday, August 6.