The French international striker joined Real Madrid for 35 million euros in July last year, but has struggled to fulfill his potential and hold down a regular first-team place in Jose Mourinho's team this season.
Tottenham boss Harry Redknapp is keen to strengthen his squad in January, with Spurs flying high after a 3-2 derby win against Arsenal and a Champions League win against Inter Milan put trophies very much on the agenda.
Benzema has been capped 32 times by France, and scored at Wembley last week as Laurent Blanc's team beat England 2-1.
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Seattle Sounders striker Steve Zakuani will train with Everton ahead of next year's MLS season and could be given the chance to slip on a blue shirt.
The 22-year-old plays internationally for Congo, but lived in England from the age of four.
Source: DSG
