Newcastle United were said to be keen to reunite Paqueta with former Lyon and Brazil team-mate Bruno Guimaraes and Arsenal have watched the midfielder on several occasions over the last year.
Speaking about Paqueta’s future last month, Lyon president Jean-Michel Aulas said: “There are proposals for him.
“There are certain players who can feel complete in the project, and others who don’t.
“Economically, we have the means to pursue our ideas and objectives.”
Chelsea and Spurs have also been credited with an interest in Paqueta during that time but it is West Ham that have made the first official move to bring him to the Premier League.
The Hammers have confirmed they have made a £33.7million offer for the 33-times capped Brazil star as they look to make him their eight signing of a hectic summer transfer window.
Hammers boss David Moyes has already added the likes of Sassuolo striker Gianluca Scamacca and Burnley winger Maxwel Cornet to his squad at a reported total cost of around £125million.
That figure could move towards the £160million-mark after Moyes confirmed a bid had been submitted for Paqueta during his pre-match press conference ahead of Thursday night’s Europa Conference League qualifying round second leg tie against Viborg.
“I’m not talking about him but I can tell you we have bid for him, yes,” explained Moyes.
“(He is) twenty three, 30 Brazil caps, can play ten, eight, plays as a false nine for Brazil quite often.
“I think his pedigree is really good, your pedigree doesn’t always guarantee it works but you’d hope that it helps towards possibly getting better.”