Sporting midfielder William Carvalho has agreed a five-year deal to join West Ham, the Daily Express have reported.
The 25-year-old is reportedly determined to make the switch to the Premier League, but a fee between the two clubs has not yet been agreed.
The Hammers thought they had completed negotiations with a £32m bid last week, but Sporting have now upped their demands to £36.5m.
After West Ham were emphatically beaten by Manchester United at Old Trafford in their opening Premier League game, and then fell to a late defeat against Southampton, Sporting could be looking to capitalise on any desperation to complete what would be a record signing.
However, the London club are still believed to be confident that a deal will be completed before the close of the transfer window.
The transfer could also hinge on Sporting's Champions League qualification, ahead of their second leg tie against Steaua Bucharest on Wednesday.
West Ham boss Slaven Bilic sees Carvalho as the perfect option to play as a holding midfielder in a 4-3-3 system.
The Portuguese international, who rose to prominence through Sporting's youth academy, has also been linked with a move to a number of other Premier League clubs.
Manchester United and Arsenal have previously been linked for Carvalho, who last summer helped Portugal win the European Championship in France.