The Hammers have been tracking the Dutch international in recent weeks following his impressive showing for Unai Emery’s side last season.
Danjuma netted 16 goals in all competitions as the Yellow Submarine reached the Champions League semi finals and enjoyed a solid La Liga campaign.
However, transfer talks have broken down, as Danjuma has rejected the personal terms on offer at the London Stadium.
West Ham are unwilling to change their contract offer to the former Bournemouth winger and they will now look elsewhere for attacking reinforcements.
Kluivert is into the final year of his contract in Rome and he represents a cheaper option than Danjuma at around €14m.