Texas Rangers owner Tom Hicks had set a personal deadline of 5 p.m. EST Tuesday for a deal to be consummated.
"There is nothing further to report relating to the consummation of a transaction involving Alex Rodriguez. No further discussions regarding this transaction are planned," the Red Sox said in a statement issued by co-owners John Henry and Tom Werner.
Commissioner Bud Selig had set a deadline for last Thursday. The teams settled on the players involved, including Boston slugger Manny Ramirez, but the union rejected an agreement between the Red Sox and Rodriguez to restructure the seven years and $179 million left on his 10-year, $252 million contract.
Hicks reportedly reduced his demand of money in the trade. Rodriguez, the reigning American League MVP, has a no-trade clause.