Beşiktaş are interested in Chilean international Isla according to Turkish sports channel NTV Spor.
Isla spent last season on loan from Juventus at Premier League outfit QPR providing two assists in 27 appearances.
The 27-year-old right-back is currently on international duty with Chile at the Copa America.
Copa America hosts Chile are currently first in Group A on four points – level with Bolivia.
Şenol Güneş was appointed Beşiktaş manager on a two-year deal last week and stated that the team need strengthening in a number of positions including the fullback position.
The Istanbul giants struggled at right-back last season. Turkish international Serdar Kurtuluş did not have a replacement and Slaven Bilic was forced to play central midfielders Necip Uysal and Atiba Hutchinson as a fullback to fill the void when he was not available.
Beşiktaş finished the league season in third place and booked a place in the Europa League group stages.