Annacone coached Pete Sampras in the second half of his career

Chief executive Roger Draper told Five Live Sport on Friday that the LTA is talking to the American.

"Obviously both sides are serious about him joining because of the length of the discussions," said Henman.

"I can only talk about the impact he's had on me and that in his quiet, understated way, he has had an enormous effect on my thought-making processes."

Draper has been conducting a radical overhaul of the structure of British tennis and American Annacone is in the frame to head up the men's game.

"We're talking with Paul. We'd like to think he's in the running. He's certainly in the mix," said Draper.

We've set out right from the outset to get a top-class team in place LTA chief executive Roger Draper

The restructure began when performance chief David Felgate was sacked in May.

"We set the bar extremely high in terms of credibility and quality of coaches who'd worked with Grand Slam winners and top 10 players," said Draper.

"Clearly Paul falls into that category but there are a few others as well."

Annacone, who used to coach Pete Sampras, has been working with Henman since December 2003.

If he does team up with the LTA, it will be the second high-profile addition to the organisation after Brad Gilbert was hired to coach Andy Murray and to help with the development of junior players.

Peter Lundgren, a former coach of Roger Federer and Marat Safin, worked with the GB team at the recent Davis Cup tie against Ukraine, and has also been linked with a permanent post with the LTA.

Draper's dismantling of the old structure will culminate with the unveiling of the new management team next month.

Recruitment firm Rockpools have been conducting a wide-ranging and rigorous search to fill the nine senior posts - ranging from head of men's and women's tennis to commercial director - that will form the backbone of the LTA's efforts to re-invigorate tennis in Britain.

Just under 300 applications have been processed with a long list of 60 going forward for interviews, which are currently taking place.

The candidates have undergone 90-minute interviews and have also had to face psychometric tests.

"We've had internal candidates, external candidates, people from this country and people from other countries - it's a world-class list," Dave Fielding, head of sports practice at Rockpools told BBC Sport.

"It's been a very thorough process but we're trying to make sure that we get the right team."

The short-listed candidates will be invited to return to face an LTA panel in mid-November with an announcement of the new team expected soon after.

"We're investigating the possibilities," Draper said. "But obviously more detailed discussions need to take place.