Great Britain got their wish and landed a home tie for the first time since 2002 when the draw for the Davis Cup Euro/Africa Zone was made on Thursday.
Jeremy Bates' side, beaten 5-0 by Switzerland at the weekend, face either Serbia & Montenegro or Israel in April.
The two countries will meet in Tel Aviv in February to decide who Britain play.
The Lawn Tennis Association (LTA) has yet to decide a venue but Glasgow has been tipped as a potential host after the emergence of Scot Andy Murray.
"There are a number of considerations we need to bear in mind before we choose a venue," an LTA spokesman told BBC Sport.
"For instance, we need to look at the players available to us and work out what surface suits them best."
The Serbians will start as favourites against Israel to set up arguably the toughest tie Britain could have faced in the draw.
They include rising star 18-year-old Novak Djokovic, who is ranked 81 in the world and has reached the third round of two Grand Slams this year.
And the Serbians would also pose a threat to Greg Rusedski and Andy Murray on the doubles court in the shape of world 11th-ranked doubles player Nenad Zimonjic.
A tie against Israel would provide a quick rematch of last April's 3-2 win in Tel Aviv in which Murray made his Cup debut.
Victory would again put Britain through to September's World Group play-offs - the stage at which they were knocked out this year by a Roger Federer-inspired Switzerland.
The tie in Geneva was Britain's sixth successive away draw following the home tie against Thailand in September three years ago.
But GB Davis Cup captain Jeremy Bates admitted mixed feelings over the draw.
"We haven't been at home for so long it's a huge bonus, but the draw could have been bit easier for us," he said.
"The Serbians have got a number of players ranked around the top 100 while Israel have got a new singles line-up which will make them tougher."
But Bates said he is determined to steer his team back into the big-time and win a match in the World Group proper for the first time in since 1986.
Bates was part of the GB side that breezed to a 4-1 win over Spain in Telford before falling to Australia in the quarter-finals nearly 20 years ago.
"We have had two guys in the top for 10 years and we still have not been able to get through the barrier since 1986," he said.
"But I don't think there is any doubt in anybody's mind that we have the belief to achieve that target.
"You need a bit of luck in the draw and a lot of momentum and a whole tie can hinge on very little."
This year, unfancied Slovakia and Croatia set up the most surprising Davis Cup final in history.
"I do not need to see Slovakia in (this year's) final to know the opportunity is out there," Bates added.