"But there's no rush, there's not another match for four months. It's important they take their time and get the right person - and I'm sure they will."
Former Davis Cup captain David Lloyd, younger brother of John, has already expressed an interest in the position he previously held for five years between 1995 and 2000.
"I've always said I would love to do it, I'm British, I love the game," said Lloyd, who owns a network of indoor tennis facilities and health clubs across the country.
"I've spent and made a lot of money building indoor courts. In life, we have to give back."
However, BBC tennis correspondent Jonathan Overend says former British number one Greg Rusedski, who is now the LTA's talent and performance ambassador, is the leading candidate to replace Lloyd.
"Tim Henman has ruled himself out for the next few years, while [Andy Murray's former coach] Mark Petchey won't work with [LTA chief executive] Roger Draper under the current regime," added Overend.
LLOYD'S DAVIS CUP RECORD
08/03/10 Lithuania 2-3 defeat
20/09/09 Poland 2-3 defeat
08/03/09 Ukraine 1-4 defeat
21/09/08 Austria 2-3 defeat
10/02/08 Argentina 1-4 defeat
23/09/07 Croatia 4-1 win
08/04/07 Netherlands 4-1 win
24/09/06 Ukraine 3-2 win
"Greg Rusedski is the bookies' favourite and was sounded out earlier this month but he's hardly on Andy Murray's Christmas card list, which surely has to be crucial."
Murray's coach Miles Maclagan has also been touted as a potential candidate, although the Scot said he does not want him to be considered for the job.
"There are a quite a few guys being talked about with Miles being one of them, which I'm not a huge fan of happening," added the 22-year-old.
"You never know what's going to happen. I've not spoken to any of the potential captains about it, but it will be interesting to see what they do."
Lloyd took over from Jeremy Bates, who resigned in the wake of a defeat by Israel, and he began promisingly, with wins over Ukraine, the Netherlands and Croatia.
However, he was unable to sustain that momentum as the retirement of Rusedski and Henman severely hit the strength in depth at his disposal.
Murray hopes to have say in Lloyd replacement
Even the presence of Murray failed to arrest Britain's slump and the 22-year-old decided to sit out the humbling defeat by Lithuania earlier this month.
That defeat - against a country with only three world-ranked singles players - led Draper to ask the organisation's player director Steven Martens to review the team's dismal performance.
The conclusions of that review will be heard later this month but rather than wait to hear them Lloyd has opted to step down, while Paul Annacone has left his position as Davis Cup coach and will focus on his role as head coach of men's tennis.
"My initial findings from the review recognise that he is not to blame for our current lack of depth in the men's game and so I am widening my review to look across men's tennis," said Martens.
However, Petchey criticised the LTA's decision to investigate internally, suggesting Draper should take full responsibility for the failure.
"I honestly believe it has to go to the top," Petchey told BBC Radio 5 live. "He [Draper] is the one who has employed these people.
"John Lloyd has become a scapegoat, he was only given the players, he had no power. We've become a laughing stock.
"We've asked the guy who has been running the programme for the last four years to do the internal review. Can you imagine what he is going to say? That I've come to the conclusion that I'm not very good at my job?"
Belgian Martens will also be charged with finding Lloyd's replacement before the vital Euro-Africa Zone Group Two relegation play-off against Turkey in Eastbourne in July.
Defeat in that tie would result in the British team being relegated to the lowest tier of the Davis Cup competition - a group including tennis minnows Albania, Luxembourg, Malta and San Marino.
"Davis Cup captaincy is a tough job and I'm sure that the next captain will be as passionate as I was and have no doubt that the team is capable of defeating Turkey in July," added Lloyd.
Draper should leave LTA - Petchey
Henman has already distanced himself from the role and before Lloyd's resignation, Martens told BBC Sport there had been no direct contact with Rusedski, who has been linked to the job.
Draper, whose own role at the helm of British tennis has been under pressure, said Lloyd's commitment had never been in doubt.
"I would like to thank John for all his efforts and, in particular, recognise his real achievement in guiding the team back into the World Group of the Davis Cup," he stated.
"He has always shown great passion and enthusiasm as captain."
With Murray having declared himself unavailable for the tie in Lithuania, Lloyd picked a team of Dan Evans, Ken Skupski, Colin Fleming and James Ward.
Going into the final day, Great Britain led 2-1 but Ward and Evans lost their singles matches to bring about a humiliating 3-2 defeat, which Lloyd conceded left him feeling "devastated".
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