The Algerian has previously been linked with the likes of Crystal Palace and Everton after impressing in Portugal since moving there in 2014.
Now, according to O Jogo, West Ham are tracking the 27-year-old too after sending scouts to watch him in action.
The Hammers are expected to bring in a number of recruits this summer to bolster their squad for next season.
Brahimi is a player who has previously been on their radar and they now want to look at him closely ahead of a concrete offer.
West Ham scouts were reportedly at Porto's game on Saturday against Belenenses and they would have been impressed with Brahimi as he got on the scoresheet in a 3-0 win.