Gilchrist's six catches in the first Test win over Pakistan in Perth last weekend lifted him to 272 dismissals and equal-fifth on the all-time Test list with former West Indies 'keeper Jeff Dujon.
Gilchrist is on target to pass England's Alec Stewart (277) in the Melbourne Boxing Day Test against Pakistan, leaving just Australians Healy (395) and Rod Marsh (355) and South African Mark Boucher (290) ahead of him.
His average of 4.32 dismissals a match is well above the top stumpers - Boucher averaged 3.82 a match, Marsh 3.70, Dujon 3.35, Healy 3.32 and Stewart 2.94 in the 82 Tests he played as a wicketkeeper.
Healy said he had "no problem" with his predecessor claiming his record.
"I am sure he can get somewhere between 400 to 450 (dismissals), which would be a nice little aspiration for him," Healy said Tuesday.
"I'd be really pleased for it (the record) to go to him in the next two years."
Healy was confident Gilchrist, 33, could play on for up to five more years, which could put the 500-mark within reach.
"If in two or three years he wants to retire from One-dayers and concentrate solely on Test matches, he could go on for a while," he said.
"The blokes now have long careers so they will produce great careers statistically."
Healy, these days a television commentator, said Gilchrist's strengths behind the stumps were his athleticism, diving and catching, although he was continually improving when he stood up to the stumps for the spinners.
Healy said Gilchrist was the "standout" keeper in world cricket and that he would choose Sri Lanka's Kumar Sangakkara to take the gloves in next year's World XI contest against Australia, because he batted at No.3 and kept well to off-spinner Muttiah Muralitharan.