The American defender is understood to have a number of clubs back home interested in his signature.
Spector, 29, is out of contract this summer but has been offered an extension on his current deal, having broken back into the Blues line-up over the second half of the season to deputise at centre-back for Michael Morrison and then Rob Kiernan.
The versatile American is understood to be leaning towards prolonging his spell with the Championship club, who have even improved their initial offer in a bid to keep him, but a stateside return is also said to be a tempting proposition.
While an offer from the States is still to materialise, several MLS clubs are reported to be hoping to lure the Illinois-native back across the Atlantic for his first taste of the US domestic scene, having jumped straight from high school to Manchester United back in 2003.
He has featured 127 times for Birmingham across various positions since arriving from West Ham United in the summer of 2011, with 26 of those appearances coming this season, but injuries have continued to pose a problem throughout his career.
His international career, meanwhile, has stalled in recent seasons, having won the last of his 34 caps in February 2012, when Jurgen Klinsmann’s side recorded a famous 1-0 friendly win over Italy in Genoa.