Liverpool, as well as AC Milan and Juventus, have all reportedly enquired about the Porto winger.
Several clubs are reportedly watching the winger across Europe, with Juventus and AC Milan thought to be keeping track of his performances.
Liverpool are thought to be among those keeping an eye on him and have already been in contact with Porto to ask about a move, according to the O Jogo report.
The Reds are expected to be very busy in this summer transfer window, with Jurgen Klopp set to rebuild the squad he inherited from Brendan Rodgers to better suit his needs.
They are currently lacking any wide players, with youngsters Jordon Ibe and Sheyi Ojo the only out and out wingers in the squad.
Lazar Markovic is another, but his future is unknown after he has spent the season out on loan at Fenerbaçhe.
Brahimi would offer pace and trickery in that position, making any move a sensible one given the style Klopp is determined to employ at Anfield.
The Algerian would not be a cheap purchase though as he currently has a €60million, around £47million, release clause in his contract.