The 32-year-old is an option if the Hammers fall short in their attempts to prise England under-21 right-back Carl Jenkinson from Arsenal, either on loan or permanently.
He has been at Real since 2009, having been at Liverpool for two-and-a-half seasons, and has 58 caps for the Spanish national side, although none of these have come since 2013.
Could it happen?
Arbeloa has fallen down the pecking order at Real at right-back, already behind Dani Cavajhal, and likely also Danilo, the club's expensive new signing from Porto.
He played 35 games in all competitions, but just 22 came in La Liga, with many from the bench, accumulating just 1,100 minutes of football.
The one element in Arbeloa's favour at Real is new boss Rafa Benitez, who managed him at Liverpool - but will also want to do best by the player and could sell if the Spaniard wants out.
Benitez sold him once before, and with Arbeloa having just one year remaining on his Real Madrid contract, this summer provides a chance to cash in while they can.
He was a favourite of Jose Mourinho at Real, and Spanish newspaper Marca reported only in April that Arbeloa was a possible target for Chelsea.