However, the club have signed goalkeeper Peter Kurucz on a permanent basis.
Lucas, who has already attracted interest from relegated Newcastle and the Greeks of Olympiakos, was expected to stay after Gianfranco Zola, the manager, insisted he was confident a deal could be struck.
But a West Ham spokesman said: 'Following discussions in recent weeks which saw the out-of-contract defender seeking a one-year deal to take him up to the 2010 World Cup, the club made the 31-year-old full-back a significant offer to retain his services.
'However, he rejected the contracted proposal this week and is pursuing other opportunities.'
West Ham added that they were 'working hard on a number of transfer targets for the coming campaign,' and it is understood they are considering a move for Chilean defender Luis Jiminez, on a season-long loan from Inter Milan.
Kurucz had been on loan, from Ujpest, and the Hungarian U21 goalkeeper has agreed a four-year deal, for an undisclosed fee.
West Ham, though, will not be signing Diego Tristan, whose short contract comes to an end this summer.
Lee Bowyer, Kyel Reid, Tony Stokes and Jimmy Walker, will also be leaving.