Diarra, 29, has been looking for a new team since seeing his contract with Lokomvotiv Moscow terminated in August after a fall out with coach Leonid Kuchuk, with the likes of Celtic, Newcastle United and Queens Park Rangers all mentioned as potential suitors, per Sky Sports.
The French midfielder, who had previous spells in England with Arsenal, Chelsea and Portsmouth, has been training with West Ham for a number of weeks after a proposed move to Inter Milan broke down, and was expected to sign a short-term contract.
However, Allardyce has now conceded that a deal won’t be possible until the end of the season, declaring the news “a real shame”.
“It's not going to happen due to administration reasons, which is a real shame," he revealed following his side’s 0-0 draw at Southampton.
“FIFA regulations, apparently, so after all the work we've done to get a player of his quality with a lot to prove would have been a huge bonus for us.”
Diarra joined Real Madrid from Portsmouth in 2009 for a reported £18.88 million fee after helping the South Coast club win the FA Cup during the previous campaign, having failed to make the breakthrough at either Chelsea or Arsenal.
The 28-times capped international would go on to make 117 total appearances for the Spanish giants over the next four seasons, winning the 2011-12 La Liga title, before leaving for Anzhi Makhachkala in August 2012.
West Ham, meanwhile, were left without a recognised central midfielder on the bench for their trip to Southampton, while Cheik Kouyate has been forced to fill in at centre-back for the past two games due to injuries to Winston Reid and James Collins.