The 30-year-old Honduran has been linked with a move to the Macron Stadium since being released by Stoke City last month.
Palacios, 30, is on the hunt for a new club after leaving Stoke at the end of last season and has been training with the Philadelphia Union of MLS for the past fortnight with a view to a permanent move.
Union head coach Jim Curtin expressed his interest in a potential deal earlier this week but the former Tottenham Hotspur star’s father, Eulogio, believes he is likelier to return to England instead.
Recent reports from the likes of the Stoke Sentinel have cited Bolton’s interest in Palacios and, while his father did not name a specific club, he did tell the Honduran outlet that he thinks the experienced free agent will accept a “second division” team’s offer.
Speaking to Diez while visiting his son in Philadelphia, Eulogio said: “I do not think he is going to play in the United States because he will continue in England. He has made a life there and does not think of moving away.
“I think he will accept the proposal of a second division team of England but he has not told us anything. We do not know about Philadelphia but we do know is that he is visiting his children [while in the US].”
Palacios, who has 95 Honduras caps to his name, has struggled for form and fitness since making a £6 million switch from Tottenham to Stoke in August 2011, having managed just 38 Premier League appearances for the Potters before his release.
The former £12 million man impressed during prior spells with both Wigan Athletic and Spurs, however, and if Bolton can work out a favourable wage package then he could well prove an inspired signing.
A midfield enforcer is believed to be on manager Neil Lennon’s summer wishlist and, with no fee attached, the two-time World Cup veteran looks like a gamble worth taking.