The Arsenal star suffered a nasty ankle injury while on international duty with Chile.
Ibrox side Glasgow Rangers boss Mark Warburton has signed eight players this summer.
The 25-year-old finished as the Hoops' top goalscorer in the Scottish Premiership last season.
The midfielder featured in the pre-season friendly win over Gak 1902 on Saturday.
Watford are reportedly interested in signing Daryl Janmaat from Newcastle United in the summer transfer window.
Rangers’ Martyn Waghorn finished as the club’s top scorer last term.
The Mexican forward says he has been kept in the dark about a move to Old Trafford, despite mounting speculation over his future.
Swansea City and Celtic are the bookmakers’ two favourites to sign Shane Duffy.
Tottenham continue to be heavily linked with a move for Mario Gotze.
Lazio are reportedly interested in signing Enner Valencia from West Ham United in the summer transfer window.