According to The Mirror, the 21-year-old Yugoslavian-born midfielder is happy at the Bundesliga club but could be tempted by the lure of Champions League football at Spurs next season.
The diminutive winger is considered one of the best youngsters plying their trade in the Bundesliga and Redknapp is believed to be preparing a £14 million offer for his services.
Marin helped Bremen to a third-place finish last season, having supplied many assists for club colleagues and has since debuted for Germany in his nation's group matches at this summer's World Cup.
Promotion within the national team has been swift for Marin, after he turned down the chance to play for Bosnia and Herzegovina in favour of Germany in 2010.
Capped at under-21 level in 2007, he was later included in a provisional squad for Euro 2008 but eventually failed to make the final-cut for the competition.
Marin’s promotion to the full World Cup squad this summer is drawing attention to his talent for club's across Europe, although if Redknapp did secure his signature then the jury would obviously be out over how he would be used at White Hart Lane.
Gareth Bale's purple-patch last season has cemented his position on the left wing, while Luka Modric can also double-up as a winger.