Green, 35, racked up 251 appearances for the Hammers during his first spell at the club before joining QPR in 2012, and the former England international impressed for the R's last season despite their relegation back to the Championship.
With Adrian suspended and Darren Randolph offering no Premier League experience, manager Slaven Bilic has been looking to bring Green back to Upton Park in order to strengthen his options between the sticks.
However, The Mirror report that a deal to re-sign Green fell through last week, because Hammers defender James Collins snubbed a move to Loftus Road.
The Welsh international centre back had been seen as a makeweight in the deal to sign Green, but the 32-year-old has allegedly rejected the move to West London as he is unwilling to drop down to the Championship.
It remains to be seen whether West Ham will now make another move for Green, but with just one week of the transfer window to go, they would have to move quickly to complete a deal - and may be considering other part-exchange options to offer QPR after Collins' snub.