Dawkins, 23, trained with the Quakes during their time at Spurs.
"Simon wants to do it; Tottenham wants to do it," San Jose coach Frank Yallop told the San Jose Mercury. "Hopefully we'll have some good news soon."
The Quakes on Tuesday waived Tony Donatelli, a midfielder from the Montreal Impact who had signed in the offseason. At the least, the release gives San Jose more room under the salary cap to sign Dawkins.
Spurs boss Harry Redknapp released Dawkins in 2009 but brought him into camp this season to see if he has recovered physically.
They would like to see if he can weather the physically demanding play of MLS.