Gough, who took 229 wickets at an average of 28.39 in 58 tests between 1994 and 2003, also told Reuters that all-rounder Stuart Broad would amass more than 300 wickets in the five-day format of the game.
"Swann could go down as England's greatest spinner when he finishes his career," said the former Yorkshire captain while attending the 142nd British Open golf championship at Muirfield.
"I think he'll end up with more than 300 test wickets and Broad too," he added.
"These guys keep fit, they hardly play any county cricket any more like we did in my day. They know they only have to play seven or eight tests in the English summer and another eight or so in the winter," added Gough.
"That's all they have to play and they don't have to play one-day cricket either."
The 34-year-old Swann went into the second Ashes test against Australia at Lord's with 226 wickets to his name and added five more as the tourists were skittled out for 128 in the first innings on Friday.
Derek Underwood (297) is England's most prolific wicket-taker among spinners followed by Swann and Jim Laker on 193.
The 30-year-old Anderson picked up 10 wickets in the first test victory in Nottingham last week to take his overall tally to 317 and is closing fast on Ian 'Beefy' Botham's all-time England record of 383.
"Anderson is going to break all sorts of records," said Gough after hosting a Q&A session with golf's former world number one Nick Faldo in the MasterCard Club at Muirfield.
"Jimmy, of all the bowlers I've seen with the new ball in his hand, is the best simply because he can bowl outswingers with little change of action. I can't remember anyone ever doing that before.
"With Beefy I could tell from his action what sort of ball he was going to bowl. With Jimmy there's hardly any change, it's all down to his wrist action."
The 42-year-old Gough, who was hampered by a knee injury in the latter stages of his career, said the modern generation were helped by their high fitness levels.
"These guys don't get injuries like we used to in the old days, they can work on their fitness between matches and this is how it always should have been," he added.
"England used to be 10 years behind everyone in world cricket but it shows when you get the system right you produce world-class cricketers and it's great to see."
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