Adrian was sent off for a high boot to the chest of Jamie Vardy late on in the Hammers’ 2-1 Premier League defeat to Leicester at Upton Park on Saturday and will now serve a three-match ban.
West Ham have been on the lookout for another goalkeeper to rival Adrian for the No 1 shirt anyway, and Sky Sports claim they will now push hard to re-sign Green, who spent six years with the club before joining QPR in 2012.
Rangers, however, want to sign a replacement first, with Huddersfield’s Alex Smithies said to have undergone the first part of a medical at Loftus Road ahead of a £1.2million transfer.
Smithies started in Huddersfield’s opening-day defeat at Hull City but has not featured in their subsequent four matches, including Tuesday’s 1-1 home draw with Brighton.
He joined Huddersfield as a 17-year-old in 2007 and has since made 304 appearances.
His move to west London could pave the way for Green, 35, to rejoin the Hammers, for whom he played 241 times after joining from Norwich in 2006.