Because he plays for Barcelona might seem a poor reason for linking a player with Liverpool, one hovering ever so slightly above because he exists as far as rationales go. Often, though, it's more than enough, as seen by Liverpool already having been linked to Christian Tello, Alexis Sanchez, Pedro Rodriguez, Bojan Krkic, and—most recently and perhaps least sensibly—Cesc Fabregas so far this summer.
With the season less than a month done, that's an impressive list of rumoured links that seemed likely to remain nothing more than rumoured links. Particularly given many of those players seem to get linked to Liverpool every window, making them convenient names for rumour mongers to toss out into the void any time there's a bit of space that needs filling. Only just maybe this time around one is more than that.
Catalan outlet Sport, along with a handful of English newspapers, have begun to suggest that Liverpool have in fact—really for real this time around—already launched at lest one bid for Alexis Sanchez, Barcelona's hard working, goal scoring, 25-year-old Chilean winger. Barcelona are on record as not looking to sell him this summer, but it appears at least a small handful of clubs including Liverpool are looking to buy nonetheless.
From Italy, Juventus are believed to be considering a bid. In France, PSG are believed to have already made one. In England, Liverpool and Manchester United may both have made a formal offer for Sanchez while Tottenham look on, interested but ill placed to act on that interest as they lack the money to compete on wages with United or to offer the player Champions League action a la Liverpool.
By any measure, the capture of Sanchez would stand as a marquee signing to dwarf last summer's failed chases for Henrikh Mkhitaryan and Willian, and to equal Diego Costa. The presence of multiple suitors seems likely to drive any transfer fee at least into the €35M range, and though at present he's only on €80k a week at Barcelona, sides like PSG in United bidding for him will inevitably drive his wages up.
Even then, the total cost of his wages and transfer fee would be less than those of teammate Cesc Fabregas, who so far at least Liverpool are believed to not be interested in despite Barcelona making him available in the hopes of raising funds to acquire Atletico Madrid's Koke. Sanchez, meanwhile, seems an ideal fit for Liverpool's system, having both the attacking talent and work rate to thrive under Brendan Rodgers.
Alexis Sanchez to Liverpool sounds far fetched. It sounds like a pipe dream. It's still early and Liverpool's interest could amount to nothing, but this time around, just maybe, it isn't.