The 39-year-old former England international, who counts West Ham United, Tottenham Hotspur, Portsmouth and Sunderland among his former clubs, left Rangers by mutual consent earlier this month to hunt for another club.
The diminutive forward has scored 284 goals in a storied career and has a number of reported options with regard to his next destination.
Defoe is keen to play on for at least another six months in his career and has been linked with a number of clubs including Sunderland and fellow third tier giants Charlton Athletic.
But widespread reports in the national media have also said Oxford United have entered the race to bring Defoe to the Kassam Stadium.
Wednesday make the trip to Oxford this weekend hoping to avenge their only League One defeat at Hillsborough this season.