Both team events, particularly the Davis Cup, have suffered from top players opting out of national duty because of the cluttered schedule, but with Britain's memorable triumph over Belgium in Ghent in November fresh in the memory, Haggerty is determined to grow their appeal.
At present the annual competitions, featuring an eight-nation World Group in the Fed Cup and a 16-strong field in the Davis Cup World Group, run on designated weekends throughout the year with the finals in November.
Haggerty said the "home-and-away" format works for the earlier rounds, but wants to see the semi-finals and final played in one week at a neutral venue.
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"What would be very interesting for me is a final four concept," Haggerty, who took over as president of the world governing body from Francesco Ricci Bitti last year, told the latest edition of ITFWorld magazine.
"In the final week, generally in November, we would have the final four teams come together in a neutral location somewhere to be determined.
"We would be able to plan in advance where that is. We could have the semi-finals in the first three days, a day of rest and then three days for the final."
Another idea, he says, would be to have the champions receiving a bye in the first round of the following year's competition. Roger Federer and Stanislas Wawrinka were missing when Switzerland lost in the first round to Belgium in 2015, having won the title a few months earlier at the end of 2014.
"The players I have talked to have been very positive about that idea and I think it would cause them to play a little more than they do right now," he said.
Haggerty, formerly the CEO and President of the United States Tennis Association (USTA) also said the best of five set format for men could also be looked at.
"(The Davis Cup) is a great property, but I want to polish it a little bit," he said.
"We've got to make sure what we do resonates with the fans and spectators."
(Reporting by Martyn Herman, editing by Pritha Sarkar)
