The Sun says the Irons are poised to shatter their transfer record for the second time in a month with a deal of almost £50million for Brazilian Anderson.
The Lazio winger, 25, flew into London on Thursday night and will undergo a medical on Friday to become the big-spending Hammers' sixth and biggest signing of the summer in the next 48 hours.
West Ham have busted the bank by agreeing to pay around £41m for Anderson with a further £6m in add-ons.
It is more than double the previous biggest spend which was £24m on centre-half Issa Diop from French side Toulouse.
Anderson will join fellow new boys Andriy Yarmalenko, Jack Wilshere, Lukas Fabianski and Ryan Fredericks as part of the Hammers' new stable in a major revamp of the squad following the arrival of Manuel Pellegrini as manager.