The French club had an original offer for the USA international, believed to be around £500,000, rejected by the SPL champions.
"We've made a second bid for Edu and we've made a bid for one player in the English Championship," Sochaux assistant coach Stephane Gilli told STV. "We need an answer quickly. Our chairman has spoken to Rangers' chairman [Craig Whyte].
"Obviously we want the player but it's up to Rangers. We think he is a quality player. We need him and we need him quickly."
Edu moved to Ibrox from MLS side Toronto in 2008 for £2.6m.