Brahimi, 28, is set to see his contract expire at the end of the season after discussions between the France-born Algeria international and Porto failed to reach an agreement.
The report states that it has always been the winger's dream to play in the Premier League, with West Ham, Everton, Wolverhampton Wanderers and other Premier League clubs being linked by a series of outlets.
It is claimed that many wanted to buy Brahimi in the summer, but his third-party ownership made a move difficult to complete. But on a free, it is likely to be easier to conclude.
Back in August, ESPN claimed that West Ham had opened talks and sent an entourage to Porto in a bid to land the winger, but a move was not agreed. West Ham signed Felipe Anderson and Andriy Yarmolenko in the window.
Brahimi's stock has never been higher after helping Porto win their first league trophy for five years last season, scoring nine goals and creating seven assists from the flank.
But his dream of a Premier League move could materialise sooner rather than later, as the clock ticks on his expiring Porto contract with West Ham likely to be one of the front runners in the January window.
West Ham have two options if they are indeed looking to sign Brahimi. In January, they will be able to land him on a pre-contract basis which will cost nothing, but he will only join in the summer, or they could buy him outright. France Football claimed in the summer that Porto would accept a fee of £22million.
Have something to tell us about this article?