Last season's Europa League semi-finalists are looking for added firepower after losing their first three Premier League games of the season to Manchester City, Nottingham Forest and Brighton and Hove Albion.
West Ham have already made seven summer signings, bringing in Alphonse Areola, Flynn Downes, Nayef Aguerd, Gianluca Scamacca, Maxwel Cornet, Thilo Kehrer and Emerson Palmieri.
Paqueta has spent the last two seasons with Lyon, having joined from AC Milan in the summer of 2020.
The 24-year-old has scored 18 goals in 67 Ligue 1 appearances for Lyon, adding a further 11 assists.
"We have bid for him," Moyes said in a press conference ahead of West Ham's Europa Conference League game against Viborg on Thursday.
"He can play as a number 10, an eight, he plays as a false nine for Brazil quite often. I think his pedigree is really good.
"Pedigree doesn't always guarantee that it works, but you would hope that it helps towards him possibly getting better."
"We've bid for a lot of players and if I told you who, you would burst out laughing and say 'you're kidding'," he added.
"Maybe we've tried to go way above our station, but we have tried to get really top players because I knew we needed it.
"For us a couple of top players coming in would give everyone a lift and help ease the pressure on Declan Rice, Michail Antonio and Tomas Soucek."
Paqueta has won 33 caps for Brazil, scoring seven goals and was part of their 2019 Copa America winning squad.
