The 34-year-old left Bootham Crescent to join Manchester United back in 1998 but looks unlikely to be returning to help the Minstermen battle against relegation from the Football League.
Greening has made just 11 npower Championship appearances this season, six during a loan spell with Barnsley.
"We tried to bring him to the club and made the phone call," Nigel Worthington told the York Press. "It's not happening because they did not want to let the lad out and want to keep him with the rest of the squad.
"I will keep tabs on his situation though next week because you never know what can change in this game."
Meanwhile, Forest's in-form midfielder Henri Lansbury is a doubt for their npower Championship clash with Brighton on Saturday.
The former Arsenal midfielder sustained injuries to his shin and calf during England Under-21's 3-0 win over Romania and was taken off early on.