The Premier League quartet face competition from Italy as the race to sign one of Europe's hottest prospects heats up.
The 17-year-old attacking midfielder is currently playing for the Bilbao youth team, and appeared at the NextGen series last year.
But Bilbao's policy of youth team promotion to first-team squad means potential suitors could face a battle to take him away from the Spanish team.
Barcelona were reportedly rebuffed last year, with Lopez eager to quickly transition into a La Liga first-team squad. The competition elsewhere could hurt his chances, and the player may not want to move abroad.
But a €1m buyout clause in his contract has Premier League clubs interested.
The report claims Liverpool have expressed an interest in the teenager, but with Arsenal, City and Chelsea all scouting the attacker as well, the Merseyside club have only an outside chance of landing the midfielder.
The Spain under-18 international is just the latest in what seems to be a constant supply of hugely talented attacking midfielders from the Spanish top flight.
Isco is expected to move to the Premier League this summer, Thiago is another tipped to transition from under-21 star to national team lynchpin, while Andres Iniesta, David Silva and Santi Cazorla are already mainstays of Vicente Del Bosque's senior squad.