The British players have fallen out of the top eight in the qualifying table for the November tournament and both players must now repeat their good form of last year to retain a chance of qualification.
Henman is currently ranked 11th in the standings with Rusedski at a lowly 23rd. Rankings are based on the best performances in the calendar year and, unless Rusedski hits the phenomenal form which took him to Hanover as a replacement for the injured Andre Agassi last year, the British No 1 will miss out.
Both Agassi and Yevgeny Kafelnikov are already assured of qualification for the tournament which will leave Hanover next year and switch locations every year.
Nicolas Kiefer's Tashkent triumph saw the German rise to sixth in the Hanover race and 11th in the world rankings.
Meanwhile, the US Open champion, Serena Williams, is to be fined for pulling out of this week's Seat Open in Luxembourg. Williams, the event's top seed, withdrew blaming fatigue - costing her a fourth pounds 2,750 fine of the season.
The WTA commercial manager, John Dolan, confirmed she will be docked the money from her end-of-year bonus pool. Dolan said: "We're very disappointed because we were looking forward to having her in Luxembourg. Obviously with her win at the US Open she would have been a huge attraction."
Williams said in a statement: "Unfortunately, I cannot make the journey this week as I am mentally and physically exhausted."
The BBC has secured exclusive rights to Great Britain's Davis Cup matches home and away for the next four years. It is a major boost for the corporation following its success in retaining exclusive coverage of Wimbledon. The deal also includes several domestic tournaments.
ATP LEADING MEN'S RANKINGS: 1 A Agassi (US) 4,470pts, 2 Y Kafelnikov (Rus) 3,819, 3 P Sampras (US) 3,544, 4 T Martin (US) 2,969, 5 G Kuerten (Bra) 2,707, 6 G Rusedski (GB) 2,336, 7 T Henman (GB), 2,300, 8 M Rios (Chile) 2,276, 9 R Krajicek (Neth) 2243, 10 A Corretja (Sp) 2,161, 11 T Haas (Ger) 2,097, 12 N Kiefer (Ger) 2,064, 13 P Rafter (Aus) 1,939, 14 N Lapentti (Ec) 1,866, 15 C Moya (Sp) 1,856, 16 C Pioline (Fr) 1794, 17 T Enqvist (Swe) 1,774, 18 F Mantilla (Sp) 1,536, 19 V Spadea (US) 1,502, 20 K Kucera (Slovak) 1,496.Reuse content