Head coach Unai Emery said after that match that the club is likely to sell a couple of players this week as they look to trim the squad.
Perez is West Ham's eighth signing under new manager Manuel Pellegrini, joining Ryan Fredericks, Lukasz Fabianski, Issa Diop, Wilshere, Andriy Yarmolenko, Fabian Balbuena and Felipe Anderson in making the move to east London.
With further midfield signings on the agenda, West Ham could be tempted to cash in.
The signings of Jorginho and Mateo Kovacic have pushed the England global further down the pecking order this summer and West Ham are interested in a loan deal - although the Independent states they will face competition from Leicester.
ESPN reporter Eduardo Fdez-Abascal has stated via his official Twitter account that Perez is on the verge of moving to the Olympic Stadium, with him expected to undergo his medical ahead of signing a three-year deal worth an apparent £5m.
Sanchez's future appears to be away from Fiorentina after spending last season on loan at La Liga side Espanyol.
West Ham travel to Anfield on Sunday to take on Liverpool in the first game of the season. "I've loved my time here when I've been involved and playing, but obviously previous year I went out and played games and bonded with the Aston Villa fans, staff and players and everyone around the city, so I appreciate them for that".
"West Ham have great fans and play in an wonderful stadium, so to sign here brings me great joy".